Solve -9x^2-12x-8x^2+7+15x

$$- 9 x ^ { 2 } - 12 x - 8 x ^ { 2 } + 7 + 15 x$$

Evaluate

$$7+3x-17x^{2}$$

Solution Steps

Combine -9x^{2} and -8x^{2} to get -17x^{2}.

$$-17x^{2}-12x+7+15x$$

Combine -12x and 15x to get 3x.

$$-17x^{2}+3x+7$$

Factor

$$-17\left(x-\frac{3-\sqrt{485}}{34}\right)\left(x-\frac{\sqrt{485}+3}{34}\right)$$

Steps Using the Quadratic Formula

Combine -9x^{2} and -8x^{2} to get -17x^{2}.

$$factor(-17x^{2}-12x+7+15x)$$

Combine -12x and 15x to get 3x.

$$factor(-17x^{2}+3x+7)$$

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-17x^{2}+3x+7=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-17\right)\times 7}}{2\left(-17\right)}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\left(-17\right)\times 7}}{2\left(-17\right)}$$

Multiply -4 times -17.

$$x=\frac{-3±\sqrt{9+68\times 7}}{2\left(-17\right)}$$

Multiply 68 times 7.

$$x=\frac{-3±\sqrt{9+476}}{2\left(-17\right)}$$

Add 9 to 476.

$$x=\frac{-3±\sqrt{485}}{2\left(-17\right)}$$

Multiply 2 times -17.

$$x=\frac{-3±\sqrt{485}}{-34}$$

Now solve the equation x=\frac{-3±\sqrt{485}}{-34} when ± is plus. Add -3 to \sqrt{485}.

$$x=\frac{\sqrt{485}-3}{-34}$$

Divide -3+\sqrt{485} by -34.

$$x=\frac{3-\sqrt{485}}{34}$$

Now solve the equation x=\frac{-3±\sqrt{485}}{-34} when ± is minus. Subtract \sqrt{485} from -3.

$$x=\frac{-\sqrt{485}-3}{-34}$$

Divide -3-\sqrt{485} by -34.

$$x=\frac{\sqrt{485}+3}{34}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{3-\sqrt{485}}{34} for x_{1} and \frac{3+\sqrt{485}}{34} for x_{2}.

$$-17x^{2}+3x+7=-17\left(x-\frac{3-\sqrt{485}}{34}\right)\left(x-\frac{\sqrt{485}+3}{34}\right)$$