Solve 7x^2+4x-40

$$7 { x }^{ 2 } +4x-40$$

Factor

$$7\left(x-\frac{-2\sqrt{71}-2}{7}\right)\left(x-\frac{2\sqrt{71}-2}{7}\right)$$

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.

$$7x^{2}+4x-40=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\times 7\left(-40\right)}}{2\times 7}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 7\left(-40\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-4±\sqrt{16-28\left(-40\right)}}{2\times 7}$$

Multiply -28 times -40.

$$x=\frac{-4±\sqrt{16+1120}}{2\times 7}$$

Add 16 to 1120.

$$x=\frac{-4±\sqrt{1136}}{2\times 7}$$

Take the square root of 1136.

$$x=\frac{-4±4\sqrt{71}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-4±4\sqrt{71}}{14}$$

Now solve the equation x=\frac{-4±4\sqrt{71}}{14} when ± is plus. Add -4 to 4\sqrt{71}.

$$x=\frac{4\sqrt{71}-4}{14}$$

Divide -4+4\sqrt{71} by 14.

$$x=\frac{2\sqrt{71}-2}{7}$$

Now solve the equation x=\frac{-4±4\sqrt{71}}{14} when ± is minus. Subtract 4\sqrt{71} from -4.

$$x=\frac{-4\sqrt{71}-4}{14}$$

Divide -4-4\sqrt{71} by 14.

$$x=\frac{-2\sqrt{71}-2}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-2+2\sqrt{71}}{7} for x_{1} and \frac{-2-2\sqrt{71}}{7} for x_{2}.

$$7x^{2}+4x-40=7\left(x-\frac{2\sqrt{71}-2}{7}\right)\left(x-\frac{-2\sqrt{71}-2}{7}\right)$$

Evaluate

$$7x^{2}+4x-40$$