Solve -5x+7x^2-8

$$- 5 x + 7 x ^ { 2 } - 8$$

Factor

$$7\left(x-\frac{5-\sqrt{249}}{14}\right)\left(x-\frac{\sqrt{249}+5}{14}\right)$$

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.

$$7x^{2}-5x-8=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 7\left(-8\right)}}{2\times 7}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 7\left(-8\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-\left(-5\right)±\sqrt{25-28\left(-8\right)}}{2\times 7}$$

Multiply -28 times -8.

$$x=\frac{-\left(-5\right)±\sqrt{25+224}}{2\times 7}$$

Add 25 to 224.

$$x=\frac{-\left(-5\right)±\sqrt{249}}{2\times 7}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{249}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{5±\sqrt{249}}{14}$$

Now solve the equation x=\frac{5±\sqrt{249}}{14} when ± is plus. Add 5 to \sqrt{249}.

$$x=\frac{\sqrt{249}+5}{14}$$

Now solve the equation x=\frac{5±\sqrt{249}}{14} when ± is minus. Subtract \sqrt{249} from 5.

$$x=\frac{5-\sqrt{249}}{14}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5+\sqrt{249}}{14} for x_{1} and \frac{5-\sqrt{249}}{14} for x_{2}.

$$7x^{2}-5x-8=7\left(x-\frac{\sqrt{249}+5}{14}\right)\left(x-\frac{5-\sqrt{249}}{14}\right)$$

Evaluate

$$7x^{2}-5x-8$$