Precalculus Examples

$x^{2} - 4 x - 15 = 0$

Step 1

Add $15$ to both sides of the equation.

$x^{2} - 4 x = 15$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 2)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 4 x + {(- 2)}^{2} = 15 + {(- 2)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = 15 + {(- 2)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $15 + {(- 2)}^{2}$ .

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Step 4.2.1.1

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = 15 + 4$

Step 4.2.1.2

Add $15$ and $4$ .

$x^{2} - 4 x + 4 = 19$

Step 5

Factor the perfect trinomial square into ${(x - 2)}^{2}$ .

${(x - 2)}^{2} = 19$

Step 6

Solve the equation for $x$ .

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Step 6.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 2 = \pm \sqrt{19}$

Step 6.2

Add $2$ to both sides of the equation.

$x = \pm \sqrt{19} + 2$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{19} + 2$

Decimal Form:

$x = 6.35889894 \dots, - 2.35889894 \dots$