What number that needs to be added to both sides of the equation $x^{2} + 4 x = 96$ $x^2 + 4x = 96$ to complete the square?

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What number that needs to be added to both sides of the equation $x^{2} + 4 x = 96$ $x^2 + 4x = 96$ to complete the square?

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Answer 1 · 2015-12-15T07:42:20

The number to be added to both sides is 4.

Explanation:

Divide the coefficient of the $x$ $x$ term by $2$ $2$ , then square the result. This number will be added to both sides of the equation. For the quadratic equation $x^{2} + 4 x = 96$ $x^2+4x=96$ , the coefficient of the $x$ $x$ term is $4$ $4$ . So ${(\frac{4}{2})}^{2} = 4$ $(4/2)^2=4$ .

$x^{2} + 4 x + 4 = 96 + 4$ $x^2+4x+4=96+4$

$x^{2} + 4 x + 4 = 100$ $x^2+4x+4=100$

${(x + 2)}^{2} = 100$ $(x+2)^2=100$

Take the square root of both sides.

$x + 2 = \pm 10$ $x+2=+-10$

Subtract $2$ $2$ from both sides.

$x = - 2 \pm 10$ $x=-2+-10$

Solve for $x$ $x$ .

$x = - 2 + 10 = 8$ $x=-2+10=8$

$x = - 2 - 10 = - 12$ $x=-2-10=-12$

$x = 8, - 12$ $x=8, -12$

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What number that needs to be added to both sides of the equation $x^{2} + 4 x = 96$ $x^2 + 4x = 96$ to complete the square?

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Explanation:

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What number that needs to be added to both sides of the equation x^2 + 4x = 96x2+4x=96x^2 + 4x = 96 to complete the square?

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What number that needs to be added to both sides of the equation $x^{2} + 4 x = 96$ $x^2 + 4x = 96$ to complete the square?