Algebra Examples

5 x^{2} - 2 x = 7

$5 x^{2} - 2 x = 7$

Step 1

Subtract

$7$ from both sides of the equation.

$5 x^{2} - 2 x - 7 = 0$

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

$a = 5$ ,

$b = - 2$ , and

$c = - 7$ into the quadratic formula and solve for

$x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (5 \cdot - 7)}}{2 \cdot 5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

$- 2$ to the power of

$2$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 5 \cdot - 7}}{2 \cdot 5}$

Step 4.1.2

Multiply

$- 4 \cdot 5 \cdot - 7$ .

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Step 4.1.2.1

Multiply

$- 4$ by

$5$ .

$x = \frac{2 \pm \sqrt{4 - 20 \cdot - 7}}{2 \cdot 5}$

Step 4.1.2.2

Multiply

$- 20$ by

$- 7$ .

$x = \frac{2 \pm \sqrt{4 + 140}}{2 \cdot 5}$

Step 4.1.3

Add

$4$ and

$140$ .

$x = \frac{2 \pm \sqrt{144}}{2 \cdot 5}$

Step 4.1.4

Rewrite

$144$ as

$12^{2}$ .

$x = \frac{2 \pm \sqrt{12^{2}}}{2 \cdot 5}$

Step 4.1.5

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

$x = \frac{2 \pm 12}{2 \cdot 5}$

Step 4.2

Multiply

$2$ by

$5$ .

$x = \frac{2 \pm 12}{10}$

Step 4.3

Simplify

$\frac{2 \pm 12}{10}$ .

$x = \frac{1 \pm 6}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{7}{5}, - 1$