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

$x (8 x - 5) = 13$

Step 1

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

Simplify the left side.

Simplify $x (8 x - 5)$ .

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Move $- 5$ to the left of $x$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

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

Subtract $13$ from both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 8 \cdot - 13}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 13$ .

Multiply $- 4$ by $8$ .

$x = \frac{5 \pm \sqrt{25 - 32 \cdot - 13}}{2 \cdot 8}$

Multiply $- 32$ by $- 13$ .

$x = \frac{5 \pm \sqrt{25 + 416}}{2 \cdot 8}$

Add $25$ and $416$ .

$x = \frac{5 \pm \sqrt{441}}{2 \cdot 8}$

Rewrite $441$ as $21^{2}$ .

$x = \frac{5 \pm \sqrt{21^{2}}}{2 \cdot 8}$

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

$x = \frac{5 \pm 21}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{5 \pm 21}{16}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{13}{8}, - 1$

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

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