Math, asked by shaikhzeeshan9607, 6 months ago

Solve for x : 5 ( x - 1 ) - 2 (x + 8 ) = 0

Answers

Answered by Aaliyah007
2

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

Show less

Solution

=

1

6

=

5

Answered by cutie08
4

 \huge \mathcal \red {\underline{\underline{A}}}  \huge \mathcal \green {\underline{\underline{N}}}  \huge \mathcal \pink {\underline{\underline{S}}}  \huge \mathcal \blue {\underline{\underline{W}}}  \huge \mathcal \orange {\underline{\underline {E}}}  \huge \mathcal \purple {\underline{\underline{R}}}

Given :

5(x - 1) - 2(x + 8) = 0

To find :

The value of x

Solution :

5(x - 1) - 2(x + 8) = 0

5x - 5 - 2x - 16 = 0

3x - 21 = 0

3x = 21

x =  \frac{21}{3}

x = 7

 \implies  \texttt {Hence, the value of x is 7.}

____________________☆

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