Algebra Examples

$8 x + 5 = 36 x^{2}$

Step 1

Subtract $36 x^{2}$ from both sides of the equation.

$8 x + 5 - 36 x^{2} = 0$

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 $a = - 36$ , $b = 8$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (- 36 \cdot 5)}}{2 \cdot - 36}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 36 \cdot 5}}{2 \cdot - 36}$

Step 4.1.2

Multiply $- 4 \cdot - 36 \cdot 5$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 36$ .

$x = \frac{- 8 \pm \sqrt{64 + 144 \cdot 5}}{2 \cdot - 36}$

Step 4.1.2.2

Multiply $144$ by $5$ .

$x = \frac{- 8 \pm \sqrt{64 + 720}}{2 \cdot - 36}$

Step 4.1.3

Add $64$ and $720$ .

$x = \frac{- 8 \pm \sqrt{784}}{2 \cdot - 36}$

Step 4.1.4

Rewrite $784$ as $28^{2}$ .

$x = \frac{- 8 \pm \sqrt{28^{2}}}{2 \cdot - 36}$

Step 4.1.5

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

$x = \frac{- 8 \pm 28}{2 \cdot - 36}$

Step 4.2

Multiply $2$ by $- 36$ .

$x = \frac{- 8 \pm 28}{- 72}$

Step 4.3

Simplify $\frac{- 8 \pm 28}{- 72}$ .

$x = \frac{2 \pm 7}{18}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1}{2}, - \frac{5}{18}$