Solve 2x^2-5x-8x^2+3-x+6=

$$2 x ^ { 2 } - 5 x - 8 x ^ { 2 } + 3 - x + 6 =$$

Evaluate

$$9-6x-6x^{2}$$

Solution Steps

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}-5x+3-x+6$$

Combine -5x and -x to get -6x.

$$-6x^{2}-6x+3+6$$

Add 3 and 6 to get 9.

$$-6x^{2}-6x+9$$

Factor

$$-6\left(x-\frac{-\sqrt{7}-1}{2}\right)\left(x-\frac{\sqrt{7}-1}{2}\right)$$

Steps Using the Quadratic Formula

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$factor(-6x^{2}-5x+3-x+6)$$

Combine -5x and -x to get -6x.

$$factor(-6x^{2}-6x+3+6)$$

Add 3 and 6 to get 9.

$$factor(-6x^{2}-6x+9)$$

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.

$$-6x^{2}-6x+9=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-6\right)\times 9}}{2\left(-6\right)}$$

Square -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-6\right)\times 9}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{-\left(-6\right)±\sqrt{36+24\times 9}}{2\left(-6\right)}$$

Multiply 24 times 9.

$$x=\frac{-\left(-6\right)±\sqrt{36+216}}{2\left(-6\right)}$$

Add 36 to 216.

$$x=\frac{-\left(-6\right)±\sqrt{252}}{2\left(-6\right)}$$

Take the square root of 252.

$$x=\frac{-\left(-6\right)±6\sqrt{7}}{2\left(-6\right)}$$

The opposite of -6 is 6.

$$x=\frac{6±6\sqrt{7}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{6±6\sqrt{7}}{-12}$$

Now solve the equation x=\frac{6±6\sqrt{7}}{-12} when ± is plus. Add 6 to 6\sqrt{7}.

$$x=\frac{6\sqrt{7}+6}{-12}$$

Divide 6+6\sqrt{7} by -12.

$$x=\frac{-\sqrt{7}-1}{2}$$

Now solve the equation x=\frac{6±6\sqrt{7}}{-12} when ± is minus. Subtract 6\sqrt{7} from 6.

$$x=\frac{6-6\sqrt{7}}{-12}$$

Divide 6-6\sqrt{7} by -12.

$$x=\frac{\sqrt{7}-1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1-\sqrt{7}}{2} for x_{1} and \frac{-1+\sqrt{7}}{2} for x_{2}.

$$-6x^{2}-6x+9=-6\left(x-\frac{-\sqrt{7}-1}{2}\right)\left(x-\frac{\sqrt{7}-1}{2}\right)$$