Find the Roots (Zeros) 3x^2+66=-30x

$3 x^{2} + 66 = - 30 x$

Step 1

Add $30 x$ to both sides of the equation.

$3 x^{2} + 66 + 30 x = 0$

Step 2

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} + 66 + 30 x$ .

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

$3 (x^{2}) + 66 + 30 x = 0$

Factor $3$ out of $66$ .

$3 x^{2} + 3 \cdot 22 + 30 x = 0$

Factor $3$ out of $30 x$ .

$3 x^{2} + 3 \cdot 22 + 3 (10 x) = 0$

Factor $3$ out of $3 x^{2} + 3 \cdot 22$ .

$3 (x^{2} + 22) + 3 (10 x) = 0$

Factor $3$ out of $3 (x^{2} + 22) + 3 (10 x)$ .

$3 (x^{2} + 22 + 10 x) = 0$

Reorder terms.

$3 (x^{2} + 10 x + 22) = 0$

Step 3

Divide each term in $3 (x^{2} + 10 x + 22) = 0$ by $3$ and simplify.

Divide each term in $3 (x^{2} + 10 x + 22) = 0$ by $3$ .

$\frac{3 (x^{2} + 10 x + 22)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x^{2} + 10 x + 22)}{3} = \frac{0}{3}$

Divide $x^{2} + 10 x + 22$ by $1$ .

$x^{2} + 10 x + 22 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x^{2} + 10 x + 22 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 1$ , $b = 10$ , and $c = 22$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 22)}}{2 \cdot 1}$

Step 6

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 22}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 22$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 22}}{2 \cdot 1}$

Multiply $- 4$ by $22$ .

$x = \frac{- 10 \pm \sqrt{100 - 88}}{2 \cdot 1}$

Subtract $88$ from $100$ .

$x = \frac{- 10 \pm \sqrt{12}}{2 \cdot 1}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$x = \frac{- 10 \pm \sqrt{4 (3)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 3}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{3}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 2 \sqrt{3}}{2}$

Simplify $\frac{- 10 \pm 2 \sqrt{3}}{2}$ .

$x = - 5 \pm \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm \sqrt{3}$

Decimal Form:

$x = - 3.26794919 \dots, - 6.73205080 \dots$

Step 8

Find the Roots (Zeros) 3x^2+66=-30x

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