Algebra Examples

$x^{2} - 8 x = - 15$

Step 1

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 2

Add the term to each side of the equation.

$x^{2} - 8 x + {(- 4)}^{2} = - 15 + {(- 4)}^{2}$

Step 3

Simplify the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

$x^{2} - 8 x + 16 = - 15 + {(- 4)}^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 15 + {(- 4)}^{2}$ .

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Step 3.2.1.1

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

$x^{2} - 8 x + 16 = - 15 + 16$

Step 3.2.1.2

Add $- 15$ and $16$ .

$x^{2} - 8 x + 16 = 1$

Step 4

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

${(x - 4)}^{2} = 1$

Step 5

Solve the equation for $x$ .

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Step 5.1

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

$x - 4 = \pm \sqrt{1}$

Step 5.2

Any root of $1$ is $1$ .

$x - 4 = \pm 1$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.3.1

First, use the positive value of the $\pm$ to find the first solution.

$x - 4 = 1$

Step 5.3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 5.3.2.1

Add $4$ to both sides of the equation.

$x = 1 + 4$

Step 5.3.2.2

Add $1$ and $4$ .

$x = 5$

Step 5.3.3

Next, use the negative value of the $\pm$ to find the second solution.

$x - 4 = - 1$

Step 5.3.4

Move all terms not containing $x$ to the right side of the equation.

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Step 5.3.4.1

Add $4$ to both sides of the equation.

$x = - 1 + 4$

Step 5.3.4.2

Add $- 1$ and $4$ .

$x = 3$

Step 5.3.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 5, 3$