Algebra Examples

$x^{2} + 14 x = 15$

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 $b$ .

${(\frac{b}{2})}^{2} = {(7)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 14 x + {(7)}^{2} = 15 + {(7)}^{2}$

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 $7$ to the power of $2$ .

$x^{2} + 14 x + 49 = 15 + {(7)}^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $15 + {(7)}^{2}$ .

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Step 3.2.1.1

Raise $7$ to the power of $2$ .

$x^{2} + 14 x + 49 = 15 + 49$

Step 3.2.1.2

Add $15$ and $49$ .

$x^{2} + 14 x + 49 = 64$

Step 4

Factor the perfect trinomial square into ${(x + 7)}^{2}$ .

${(x + 7)}^{2} = 64$

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.

$x + 7 = \pm \sqrt{64}$

Step 5.2

Simplify $\pm \sqrt{64}$ .

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Step 5.2.1

Rewrite $64$ as $8^{2}$ .

$x + 7 = \pm \sqrt{8^{2}}$

Step 5.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x + 7 = \pm 8$

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.

$x + 7 = 8$

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

Subtract $7$ from both sides of the equation.

$x = 8 - 7$

Step 5.3.2.2

Subtract $7$ from $8$ .

$x = 1$

Step 5.3.3

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

$x + 7 = - 8$

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

Subtract $7$ from both sides of the equation.

$x = - 8 - 7$

Step 5.3.4.2

Subtract $7$ from $- 8$ .

$x = - 15$

Step 5.3.5

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

$x = 1, - 15$