@kingaditiyasharma
Answers
Answer:
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8
{\color{#c92786}{(x-2)(x+2)}}+1=2x-3x+8x
(x−2)(x+2)+1=2x−3x+8x
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2
(
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2
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2
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{\color{#c92786}{x(x+2)-2(x+2)}}+1=2x-3x+8x
x(x+2)−2(x+2)+1=2x−3x+8x
2
Distribute
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(
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2
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{\color{#c92786}{x(x+2)}}-2(x+2)+1=2x-3x+8x
x(x+2)−2(x+2)+1=2x−3x+8x
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2
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+
1
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{\color{#c92786}{x^{2}+2x}}-2(x+2)+1=2x-3x+8x
x2+2x−2(x+2)+1=2x−3x+8x
3
Distribute
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2
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2
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2
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+
1
=
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8
x^{2}+2x{\color{#c92786}{-2(x+2)}}+1=2x-3x+8x
x2+2x−2(x+2)+1=2x−3x+8x
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x^{2}+2x{\color{#c92786}{-2x-4}}+1=2x-3x+8x
x2+2x−2x−4+1=2x−3x+8x
4
Combine like terms
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2
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x^{2}+{\color{#c92786}{2x}}{\color{#c92786}{-2x}}-4+1=2x-3x+8x
x2+2x−2x−4+1=2x−3x+8x
2
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4
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1
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x^{2}{\color{#c92786}{-4}}+1=2x-3x+8x
x2−4+1=2x−3x+8x
5
Add the numbers
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4
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1
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x^{2}{\color{#c92786}{-4}}+{\color{#c92786}{1}}=2x-3x+8x
x2−4+1=2x−3x+8x
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x^{2}{\color{#c92786}{-3}}=2x-3x+8x
x2−3=2x−3x+8x
6
Combine like terms
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3
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x^{2}-3={\color{#c92786}{2x}}{\color{#c92786}{-3x}}+{\color{#c92786}{8x}}
x2−3=2x−3x+8x
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3
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7
x^{2}-3={\color{#c92786}{7x}}
x2−3=7x
7
Move terms to the left side
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3
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7
x^{2}-3=7x
x2−3=7x
2
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3
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7
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0
x^{2}-3-7x=0
x2−3−7x=0
8
Rearrange terms
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3
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7
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0
x^{2}-3-7x=0
x2−3−7x=0
2
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7
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3
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0
x^{2}-7x-3=0
x2−7x−3=0
9
Use the quadratic formula
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x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
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7
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3
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0
x^{2}-7x-3=0
x2−7x−3=0
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1
a={\color{#c92786}{1}}
a=1
=
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7
b={\color{#e8710a}{-7}}
b=−7
=
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3
c={\color{#129eaf}{-3}}
c=−3
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7
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±
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2
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⋅
1
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⋅
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x=\frac{-({\color{#e8710a}{-7}}) \pm \sqrt{({\color{#e8710a}{-7}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-3}})}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−(−7)±(−7)2−4⋅1(−3)
10
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Multiply the numbers
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7
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x=\frac{7 \pm \sqrt{61}}{2}
x=27±61
11
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
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7
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6
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x=\frac{7+\sqrt{61}}{2}
x=27+61
=
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x=\frac{7-\sqrt{61}}{2}
x=27−61
12
Solve
Rearrange and isolate the variable to find each solution
=
7
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6
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√
2
x=\frac{7+\sqrt{61}}{2}
x=27+61
=
7
−
6
1
√
2
x=\frac{7-\sqrt{61}}{2}
x=27−61
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Solution
=
7
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6
1
√
2