Algebra Examples

$x^{2} + 8 x + 9 = 0$

Step 1

Subtract $9$ from both sides of the equation.

$x^{2} + 8 x = - 9$

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 $b$ .

${(\frac{b}{2})}^{2} = {(4)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 8 x + {(4)}^{2} = - 9 + {(4)}^{2}$

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 $4$ to the power of $2$ .

$x^{2} + 8 x + 16 = - 9 + {(4)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 9 + {(4)}^{2}$ .

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Step 4.2.1.1

Raise $4$ to the power of $2$ .

$x^{2} + 8 x + 16 = - 9 + 16$

Step 4.2.1.2

Add $- 9$ and $16$ .

$x^{2} + 8 x + 16 = 7$

Step 5

Factor the perfect trinomial square into ${(x + 4)}^{2}$ .

${(x + 4)}^{2} = 7$

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.

$x + 4 = \pm \sqrt{7}$

Step 6.2

Subtract $4$ from both sides of the equation.

$x = \pm \sqrt{7} - 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{7} - 4$

Decimal Form:

$x = - 1.35424868 \dots, - 6.64575131 \dots$