Solve 8x^2+7x+2*quadx+2

$$8 x ^ { 2 } + 7 x + 2 \times \quad x + 2$$

Factor

$$8\left(x-\frac{-\sqrt{17}-9}{16}\right)\left(x-\frac{\sqrt{17}-9}{16}\right)$$

Steps Using the Quadratic Formula

Combine 7x and 2x to get 9x.

$$factor(8x^{2}+9x+2)$$

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.

$$8x^{2}+9x+2=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}-4\times 8\times 2}}{2\times 8}$$

Square 9.

$$x=\frac{-9±\sqrt{81-4\times 8\times 2}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-9±\sqrt{81-32\times 2}}{2\times 8}$$

Multiply -32 times 2.

$$x=\frac{-9±\sqrt{81-64}}{2\times 8}$$

Add 81 to -64.

$$x=\frac{-9±\sqrt{17}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-9±\sqrt{17}}{16}$$

Now solve the equation x=\frac{-9±\sqrt{17}}{16} when ± is plus. Add -9 to \sqrt{17}.

$$x=\frac{\sqrt{17}-9}{16}$$

Now solve the equation x=\frac{-9±\sqrt{17}}{16} when ± is minus. Subtract \sqrt{17} from -9.

$$x=\frac{-\sqrt{17}-9}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-9+\sqrt{17}}{16} for x_{1} and \frac{-9-\sqrt{17}}{16} for x_{2}.

$$8x^{2}+9x+2=8\left(x-\frac{\sqrt{17}-9}{16}\right)\left(x-\frac{-\sqrt{17}-9}{16}\right)$$

Evaluate

$$8x^{2}+9x+2$$

Solution Steps

Combine 7x and 2x to get 9x.

$$8x^{2}+9x+2$$