Solve Using the Quadratic Formula x(5x-8)=13

$x (5 x - 8) = 13$

Step 1

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

Simplify the left side.

Simplify $x (5 x - 8)$ .

Simplify by multiplying through.

Apply the distributive property.

$x (5 x) + x \cdot - 8 = 13$

Reorder.

Rewrite using the commutative property of multiplication.

$5 x \cdot x + x \cdot - 8 = 13$

Move $- 8$ to the left of $x$ .

$5 x \cdot x - 8 \cdot x = 13$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$5 (x \cdot x) - 8 \cdot x = 13$

Multiply $x$ by $x$ .

$5 x^{2} - 8 \cdot x = 13$

$5 x^{2} - 8 x = 13$

Subtract $13$ from both sides of the equation.

$5 x^{2} - 8 x - 13 = 0$

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 $a = 5$ , $b = - 8$ , and $c = - 13$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (5 \cdot - 13)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 5 \cdot - 13}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 13$ .

Multiply $- 4$ by $5$ .

$x = \frac{8 \pm \sqrt{64 - 20 \cdot - 13}}{2 \cdot 5}$

Multiply $- 20$ by $- 13$ .

$x = \frac{8 \pm \sqrt{64 + 260}}{2 \cdot 5}$

Add $64$ and $260$ .

$x = \frac{8 \pm \sqrt{324}}{2 \cdot 5}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{8 \pm \sqrt{18^{2}}}{2 \cdot 5}$

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

$x = \frac{8 \pm 18}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{8 \pm 18}{10}$

Simplify $\frac{8 \pm 18}{10}$ .

$x = \frac{4 \pm 9}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{13}{5}, - 1$

Solve Using the Quadratic Formula x(5x-8)=13

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