Algebra Examples

$x^{2} - 2 x + 7 = 4 x - 10$

Step 1

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

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Step 1.1

Subtract $4 x$ from both sides of the equation.

$x^{2} - 2 x + 7 - 4 x = - 10$

Step 1.2

Subtract $4 x$ from $- 2 x$ .

$x^{2} - 6 x + 7 = - 10$

Step 2

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

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Step 2.1

Add $10$ to both sides of the equation.

$x^{2} - 6 x + 7 + 10 = 0$

Step 2.2

Add $7$ and $10$ .

$x^{2} - 6 x + 17 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 1$ , $b = - 6$ , and $c = 17$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 17)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 17}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 17$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 17}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $17$ .

$x = \frac{6 \pm \sqrt{36 - 68}}{2 \cdot 1}$

Step 5.1.3

Subtract $68$ from $36$ .

$x = \frac{6 \pm \sqrt{- 32}}{2 \cdot 1}$

Step 5.1.4

Rewrite $- 32$ as $- 1 (32)$ .

$x = \frac{6 \pm \sqrt{- 1 \cdot 32}}{2 \cdot 1}$

Step 5.1.5

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$x = \frac{6 \pm \sqrt{- 1} \cdot \sqrt{32}}{2 \cdot 1}$

Step 5.1.6

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

$x = \frac{6 \pm i \cdot \sqrt{32}}{2 \cdot 1}$

Step 5.1.7

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 5.1.7.1

Factor $16$ out of $32$ .

$x = \frac{6 \pm i \cdot \sqrt{16 (2)}}{2 \cdot 1}$

Step 5.1.7.2

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

$x = \frac{6 \pm i \cdot \sqrt{4^{2} \cdot 2}}{2 \cdot 1}$

Step 5.1.8

Pull terms out from under the radical.

$x = \frac{6 \pm i \cdot (4 \sqrt{2})}{2 \cdot 1}$

Step 5.1.9

Move $4$ to the left of $i$ .

$x = \frac{6 \pm 4 i \sqrt{2}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{6 \pm 4 i \sqrt{2}}{2}$

Step 5.3

Simplify $\frac{6 \pm 4 i \sqrt{2}}{2}$ .

$x = 3 \pm 2 i \sqrt{2}$

Step 6