Solve by Factoring 5x^2+16x+3=5x

$5 x^{2} + 16 x + 3 = 5 x$

Subtract $5 x$ from both sides of the equation.

$5 x^{2} + 16 x + 3 - 5 x = 0$

Subtract $5 x$ from $16 x$ .

$5 x^{2} + 11 x + 3 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 5$ , $b = 11$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (5 \cdot 3)}}{2 \cdot 5}$

Simplify.

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 11 \pm \sqrt{121 - 20 \cdot 3}}{2 \cdot 5}$

Multiply $- 20$ by $3$ .

$x = \frac{- 11 \pm \sqrt{121 - 60}}{2 \cdot 5}$

Subtract $60$ from $121$ .

$x = \frac{- 11 \pm \sqrt{61}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 11 \pm \sqrt{61}}{10}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 11 \pm \sqrt{121 - 20 \cdot 3}}{2 \cdot 5}$

Multiply $- 20$ by $3$ .

$x = \frac{- 11 \pm \sqrt{121 - 60}}{2 \cdot 5}$

Subtract $60$ from $121$ .

$x = \frac{- 11 \pm \sqrt{61}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 11 \pm \sqrt{61}}{10}$

Change the $\pm$ to $+$ .

$x = \frac{- 11 + \sqrt{61}}{10}$

Rewrite $- 11$ as $- 1 (11)$ .

$x = \frac{- 1 \cdot 11 + \sqrt{61}}{10}$

Factor $- 1$ out of $\sqrt{61}$ .

$x = \frac{- 1 \cdot 11 - 1 (- \sqrt{61})}{10}$

Factor $- 1$ out of $- 1 (11) - 1 (- \sqrt{61})$ .

$x = \frac{- 1 (11 - \sqrt{61})}{10}$

Move the negative in front of the fraction.

$x = - \frac{11 - \sqrt{61}}{10}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 11 \pm \sqrt{121 - 20 \cdot 3}}{2 \cdot 5}$

Multiply $- 20$ by $3$ .

$x = \frac{- 11 \pm \sqrt{121 - 60}}{2 \cdot 5}$

Subtract $60$ from $121$ .

$x = \frac{- 11 \pm \sqrt{61}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 11 \pm \sqrt{61}}{10}$

Change the $\pm$ to $-$ .

$x = \frac{- 11 - \sqrt{61}}{10}$

Rewrite $- 11$ as $- 1 (11)$ .

$x = \frac{- 1 \cdot 11 - \sqrt{61}}{10}$

Factor $- 1$ out of $- \sqrt{61}$ .

$x = \frac{- 1 \cdot 11 - (\sqrt{61})}{10}$

Factor $- 1$ out of $- 1 (11) - (\sqrt{61})$ .

$x = \frac{- 1 (11 + \sqrt{61})}{10}$

Move the negative in front of the fraction.

$x = - \frac{11 + \sqrt{61}}{10}$

The final answer is the combination of both solutions.

$x = - \frac{11 - \sqrt{61}}{10}, - \frac{11 + \sqrt{61}}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11 - \sqrt{61}}{10}, - \frac{11 + \sqrt{61}}{10}$

Decimal Form:

$x = - 0.31897503 \dots, - 1.88102496 \dots$

Solve by Factoring 5x^2+16x+3=5x

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