Solve 8x^2+3x-2

$$8 { x }^{ 2 } +3x-2$$

Factor

$$8\left(x-\frac{-\sqrt{73}-3}{16}\right)\left(x-\frac{\sqrt{73}-3}{16}\right)$$

Steps Using the Quadratic Formula

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.

$$8x^{2}+3x-2=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 8\left(-2\right)}}{2\times 8}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times 8\left(-2\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-3±\sqrt{9-32\left(-2\right)}}{2\times 8}$$

Multiply -32 times -2.

$$x=\frac{-3±\sqrt{9+64}}{2\times 8}$$

Add 9 to 64.

$$x=\frac{-3±\sqrt{73}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-3±\sqrt{73}}{16}$$

Now solve the equation x=\frac{-3±\sqrt{73}}{16} when ± is plus. Add -3 to \sqrt{73}.

$$x=\frac{\sqrt{73}-3}{16}$$

Now solve the equation x=\frac{-3±\sqrt{73}}{16} when ± is minus. Subtract \sqrt{73} from -3.

$$x=\frac{-\sqrt{73}-3}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{73}}{16} for x_{1} and \frac{-3-\sqrt{73}}{16} for x_{2}.

$$8x^{2}+3x-2=8\left(x-\frac{\sqrt{73}-3}{16}\right)\left(x-\frac{-\sqrt{73}-3}{16}\right)$$

Evaluate

$$8x^{2}+3x-2$$