Solve 7x^2+8x-2=

$$7 { x }^{ 2 } +8x-2=$$

Factor

$$7\left(x-\frac{-\sqrt{30}-4}{7}\right)\left(x-\frac{\sqrt{30}-4}{7}\right)$$

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.

$$7x^{2}+8x-2=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 7\left(-2\right)}}{2\times 7}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 7\left(-2\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-8±\sqrt{64-28\left(-2\right)}}{2\times 7}$$

Multiply -28 times -2.

$$x=\frac{-8±\sqrt{64+56}}{2\times 7}$$

Add 64 to 56.

$$x=\frac{-8±\sqrt{120}}{2\times 7}$$

Take the square root of 120.

$$x=\frac{-8±2\sqrt{30}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-8±2\sqrt{30}}{14}$$

Now solve the equation x=\frac{-8±2\sqrt{30}}{14} when ± is plus. Add -8 to 2\sqrt{30}.

$$x=\frac{2\sqrt{30}-8}{14}$$

Divide -8+2\sqrt{30} by 14.

$$x=\frac{\sqrt{30}-4}{7}$$

Now solve the equation x=\frac{-8±2\sqrt{30}}{14} when ± is minus. Subtract 2\sqrt{30} from -8.

$$x=\frac{-2\sqrt{30}-8}{14}$$

Divide -8-2\sqrt{30} by 14.

$$x=\frac{-\sqrt{30}-4}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-4+\sqrt{30}}{7} for x_{1} and \frac{-4-\sqrt{30}}{7} for x_{2}.

$$7x^{2}+8x-2=7\left(x-\frac{\sqrt{30}-4}{7}\right)\left(x-\frac{-\sqrt{30}-4}{7}\right)$$

Evaluate

$$7x^{2}+8x-2$$