Solve 2x+8x^2-3+2x*2

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

Evaluate

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

Solution Steps

Multiply 2 and 2 to get 4.

$$2x+8x^{2}-3+4x$$

Combine 2x and 4x to get 6x.

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

Factor

$$8\left(x-\frac{-\sqrt{33}-3}{8}\right)\left(x-\frac{\sqrt{33}-3}{8}\right)$$

Steps Using the Quadratic Formula

Multiply 2 and 2 to get 4.

$$factor(2x+8x^{2}-3+4x)$$

Combine 2x and 4x to get 6x.

$$factor(6x+8x^{2}-3)$$

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.

$$8x^{2}+6x-3=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 8\left(-3\right)}}{2\times 8}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 8\left(-3\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-6±\sqrt{36-32\left(-3\right)}}{2\times 8}$$

Multiply -32 times -3.

$$x=\frac{-6±\sqrt{36+96}}{2\times 8}$$

Add 36 to 96.

$$x=\frac{-6±\sqrt{132}}{2\times 8}$$

Take the square root of 132.

$$x=\frac{-6±2\sqrt{33}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-6±2\sqrt{33}}{16}$$

Now solve the equation x=\frac{-6±2\sqrt{33}}{16} when ± is plus. Add -6 to 2\sqrt{33}.

$$x=\frac{2\sqrt{33}-6}{16}$$

Divide -6+2\sqrt{33} by 16.

$$x=\frac{\sqrt{33}-3}{8}$$

Now solve the equation x=\frac{-6±2\sqrt{33}}{16} when ± is minus. Subtract 2\sqrt{33} from -6.

$$x=\frac{-2\sqrt{33}-6}{16}$$

Divide -6-2\sqrt{33} by 16.

$$x=\frac{-\sqrt{33}-3}{8}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{33}}{8} for x_{1} and \frac{-3-\sqrt{33}}{8} for x_{2}.

$$8x^{2}+6x-3=8\left(x-\frac{\sqrt{33}-3}{8}\right)\left(x-\frac{-\sqrt{33}-3}{8}\right)$$