Algebra Examples

$x^{2} - 7 x = - 9 x - 2$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Add $9 x$ to both sides of the equation.

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

Step 1.2

Add $- 7 x$ and $9 x$ .

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

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 $b$ .

${(\frac{b}{2})}^{2} = {(1)}^{2}$

Step 3

Add the term to each side of the equation.

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

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

One to any power is one.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 2 + {(1)}^{2}$ .

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Step 4.2.1.1

One to any power is one.

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

Step 4.2.1.2

Add $- 2$ and $1$ .

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

Step 5

Factor the perfect trinomial square into ${(x + 1)}^{2}$ .

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

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.

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

Step 6.2

Rewrite $\sqrt{- 1}$ as $i$ .

$x + 1 = \pm i$

Step 6.3

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

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Step 6.3.1

Subtract $1$ from both sides of the equation.

$x = \pm i - 1$

Step 6.3.2

Reorder $\pm i$ and $- 1$ .

$x = - 1 \pm i$