Write as a Set of Linear Factors y=-3x^2-29x+30

$y = - 3 x^{2} - 29 x + 30$

Step 1

Factor $- 1$ out of $- 3 x^{2} - 29 x + 30$ .

Factor $- 1$ out of $- 3 x^{2}$ .

$y = - (3 x^{2}) - 29 x + 30$

Factor $- 1$ out of $- 29 x$ .

$y = - (3 x^{2}) - (29 x) + 30$

Rewrite $30$ as $- 1 (- 30)$ .

$y = - (3 x^{2}) - (29 x) - 1 \cdot - 30$

Factor $- 1$ out of $- (3 x^{2}) - (29 x)$ .

$y = - (3 x^{2} + 29 x) - 1 \cdot - 30$

Factor $- 1$ out of $- (3 x^{2} + 29 x) - 1 (- 30)$ .

$y = - (3 x^{2} + 29 x - 30)$

Step 2

Use the quadratic formula to find the roots for $3 x^{2} + 29 x - 30 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 3$ , $b = 29$ , and $c = - 30$ into the quadratic formula and solve for $x$ .

$y = \frac{- 29 \pm \sqrt{29^{2} - 4 \cdot (3 \cdot - 30)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $29$ to the power of $2$ .

$x = \frac{- 29 \pm \sqrt{841 - 4 \cdot 3 \cdot - 30}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 30$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 29 \pm \sqrt{841 - 12 \cdot - 30}}{2 \cdot 3}$

Multiply $- 12$ by $- 30$ .

$x = \frac{- 29 \pm \sqrt{841 + 360}}{2 \cdot 3}$

Add $841$ and $360$ .

$x = \frac{- 29 \pm \sqrt{1201}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 29 \pm \sqrt{1201}}{6}$

The final answer is the combination of both solutions.

$x = - \frac{29 - \sqrt{1201}}{6}, - \frac{29 + \sqrt{1201}}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{29 - \sqrt{1201}}{6}, - \frac{29 + \sqrt{1201}}{6}$

Decimal Form:

$x = 0.94257448 \dots, - 10.60924115 \dots$