Math, asked by GodLegendafk, 1 day ago

express both side into square and solve
a) x^2+x+(1/2)^2=(1/2)^2+6

Answers

Answered by abhinandanp81
2

Answer:

Evaluate the exponent

2

+

+

(

1

2

)

2

=

(

1

2

)

2

+

6

x^{2}+x+{\color{#c92786}{\left(\frac{1}{2}\right)^{2}}}=(\frac{1}{2})^{2}+6

x2+x+(21)2=(21)2+6

2

+

+

1

4

=

(

1

2

)

2

+

6

x^{2}+x+{\color{#c92786}{\frac{1}{4}}}=(\frac{1}{2})^{2}+6

x2+x+41=(21)2+6

2

Evaluate the exponent

2

+

+

1

4

=

(

1

2

)

2

+

6

x^{2}+x+\frac{1}{4}={\color{#c92786}{\left(\frac{1}{2}\right)^{2}}}+6

x2+x+41=(21)2+6

2

+

+

1

4

=

1

4

+

6

x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{1}{4}}}+6

x2+x+41=41+6

3

Add the numbers

2

+

+

1

4

=

1

4

+

6

x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{1}{4}}}+{\color{#c92786}{6}}

x2+x+41=41+6

2

+

+

1

4

=

2

5

4

x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{25}{4}}}

x2+x+41=425

4

Move terms to the left side

2

+

+

1

4

=

2

5

4

x^{2}+x+\frac{1}{4}=\frac{25}{4}

x2+x+41=425

2

+

+

1

4

2

5

4

=

0

x^{2}+x+\frac{1}{4}-\frac{25}{4}=0

x2+x+41−425=0

5

Subtract the numbers

2

+

+

1

4

2

5

4

=

0

x^{2}+x+{\color{#c92786}{\frac{1}{4}}}{\color{#c92786}{-\frac{25}{4}}}=0

x2+x+41−425=0

2

+

6

=

0

x^{2}+x{\color{#c92786}{-6}}=0

x2+x−6=0

6

Use the quadratic formula

=

±

2

4

2

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

+

6

=

0

x^{2}+x-6=0

x2+x−6=0

=

1

a={\color{#c92786}{1}}

a=1

=

1

b={\color{#e8710a}{1}}

b=1

=

6

c={\color{#129eaf}{-6}}

c=−6

=

1

±

1

2

4

1

(

6

)

2

1

x=\frac{-{\color{#e8710a}{1}} \pm \sqrt{{\color{#e8710a}{1}}^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-6}})}}{2 \cdot {\color{#c92786}{1}}}

x=2⋅1−1±12−4⋅1(−6)

7

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Multiply the numbers

=

1

±

5

2

x=\frac{-1 \pm 5}{2}

x=2−1±5

8

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

=

1

+

5

2

x=\frac{-1+5}{2}

x=2−1+5

=

1

5

2

x=\frac{-1-5}{2}

x=2−1−5

9

Solve

Rearrange and isolate the variable to find each solution

=

2

x=2

x=2

=

3

Answered by skatiyar654
0

Step-by-step explanation:

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