Algebra Examples

$x^{2} + 6 x = 7$

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 $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = 7 + {(3)}^{2}$

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 $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 7 + {(3)}^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $7 + {(3)}^{2}$ .

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Step 3.2.1.1

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = 7 + 9$

Step 3.2.1.2

Add $7$ and $9$ .

$x^{2} + 6 x + 9 = 16$

Step 4

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = 16$

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.

$x + 3 = \pm \sqrt{16}$

Step 5.2

Simplify $\pm \sqrt{16}$ .

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Step 5.2.1

Rewrite $16$ as $4^{2}$ .

$x + 3 = \pm \sqrt{4^{2}}$

Step 5.2.2

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

$x + 3 = \pm 4$

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.

$x + 3 = 4$

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 $3$ from both sides of the equation.

$x = 4 - 3$

Step 5.3.2.2

Subtract $3$ from $4$ .

$x = 1$

Step 5.3.3

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

$x + 3 = - 4$

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 $3$ from both sides of the equation.

$x = - 4 - 3$

Step 5.3.4.2

Subtract $3$ from $- 4$ .

$x = - 7$

Step 5.3.5

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

$x = 1, - 7$