Solve for x : 5 ( x - 1 ) - 2 (x + 8 ) = 0
Answers
Answer:
Combine multiplied terms into a single fraction
5
(
−
1
)
−
2
(
+
8
)
=
0
\frac{x}{5}(x-1)-2(x+8)=0
5x(x−1)−2(x+8)=0
(
−
1
)
5
−
2
(
+
8
)
=
0
\frac{x(x-1)}{5}-2(x+8)=0
5x(x−1)−2(x+8)=0
2
Distribute
(
−
1
)
5
−
2
(
+
8
)
=
0
\frac{{\color{#c92786}{x(x-1)}}}{5}-2(x+8)=0
5x(x−1)−2(x+8)=0
2
−
5
−
2
(
+
8
)
=
0
\frac{{\color{#c92786}{x^{2}-x}}}{5}-2(x+8)=0
5x2−x−2(x+8)=0
3
Distribute
2
−
5
−
2
(
+
8
)
=
0
\frac{x^{2}-x}{5}{\color{#c92786}{-2(x+8)}}=0
5x2−x−2(x+8)=0
2
−
5
−
2
−
1
6
=
0
\frac{x^{2}-x}{5}{\color{#c92786}{-2x-16}}=0
5x2−x−2x−16=0
4
Multiply all terms by the same value to eliminate fraction denominators
2
−
5
−
2
−
1
6
=
0
\frac{x^{2}-x}{5}-2x-16=0
5x2−x−2x−16=0
5
(
2
−
5
−
2
−
1
6
)
=
5
⋅
0
5(\frac{x^{2}-x}{5}-2x-16)=5 \cdot 0
5(5x2−x−2x−16)=5⋅0
5
Simplify
Distribute
Cancel multiplied terms that are in the denominator
Combine like terms
Multiply by zero
2
−
1
1
−
8
0
=
0
x^{2}-11x-80=0
x2−11x−80=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
−
1
1
−
8
0
=
0
x^{2}-11x-80=0
x2−11x−80=0
=
1
a={\color{#c92786}{1}}
a=1
=
−
1
1
b={\color{#e8710a}{-11}}
b=−11
=
−
8
0
c={\color{#129eaf}{-80}}
c=−80
=
−
(
−
1
1
)
±
(
−
1
1
)
2
−
4
⋅
1
(
−
8
0
)
√
2
⋅
1
x=\frac{-({\color{#e8710a}{-11}}) \pm \sqrt{({\color{#e8710a}{-11}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-80}})}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−(−11)±(−11)2−4⋅1(−80)
7
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
=
1
1
±
2
1
2
x=\frac{11 \pm 21}{2}
x=211±21
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
1
+
2
1
2
x=\frac{11+21}{2}
x=211+21
=
1
1
−
2
1
2
x=\frac{11-21}{2}
x=211−21
9
Solve
Rearrange and isolate the variable to find each solution
=
1
6
x=16
x=16
=
−
5
x=-5
x=−5
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Solution
=
1
6
=
−
5
☆ ☆
Given :
To find :
The value of x
Solution :