\[\frac{1}{2}{x}^{2}-16x=5\]

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Examples

Simplify

\frac{1}{2}{x}^{2}

\frac{{x}^{2}}{2}

\frac{{x}^{2}}{2}-16x=5

Multiply both sides by

2

{x}^{2}-32x=10

Move all terms to one side.

{x}^{2}-32x-10=0

Use the Quadratic Formula.

In general, given

a{x}^{2}+bx+c=0

, there exists two solutions where:

x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}

In this case,

a=1

b=-32

and

c=-10

{x}^{}=\frac{32+\sqrt{{(-32)}^{2}-4\times -10}}{2},\frac{32-\sqrt{{(-32)}^{2}-4\times -10}}{2}

Simplify.

x=\frac{32+2\sqrt{266}}{2},\frac{32-2\sqrt{266}}{2}

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x=\frac{32+2\sqrt{266}}{2},\frac{32-2\sqrt{266}}{2}

Simplify solutions.

x=16+\sqrt{266},16-\sqrt{266}

Done

Decimal Form: 32.309506, -0.309506

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