Algebra Examples

$x^{2} - 6 = 2 - 18 x$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Move all the expressions to the left side of the equation.

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Step 1.1.1

Subtract $2$ from both sides of the equation.

$x^{2} - 6 - 2 = - 18 x$

Step 1.1.2

Add $18 x$ to both sides of the equation.

$x^{2} - 6 - 2 + 18 x = 0$

Step 1.2

Subtract $2$ from $- 6$ .

$x^{2} - 8 + 18 x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 18$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{- 18 \pm \sqrt{18^{2} - 4 \cdot (1 \cdot - 8)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $18$ to the power of $2$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 1 \cdot - 8}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 8$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot - 8}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 8$ .

$x = \frac{- 18 \pm \sqrt{324 + 32}}{2 \cdot 1}$

Step 4.1.3

Add $324$ and $32$ .

$x = \frac{- 18 \pm \sqrt{356}}{2 \cdot 1}$

Step 4.1.4

Rewrite $356$ as $2^{2} \cdot 89$ .

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Step 4.1.4.1

Factor $4$ out of $356$ .

$x = \frac{- 18 \pm \sqrt{4 (89)}}{2 \cdot 1}$

Step 4.1.4.2

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

$x = \frac{- 18 \pm \sqrt{2^{2} \cdot 89}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{- 18 \pm 2 \sqrt{89}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 18 \pm 2 \sqrt{89}}{2}$

Step 4.3

Simplify $\frac{- 18 \pm 2 \sqrt{89}}{2}$ .

$x = - 9 \pm \sqrt{89}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 9 \pm \sqrt{89}$

Decimal Form:

$x = 0.43398113 \dots, - 18.43398113 \dots$