Solve 7x^2+x-120

$$7 { x }^{ 2 } +x-120$$

Factor

$$7\left(x-\frac{-\sqrt{3361}-1}{14}\right)\left(x-\frac{\sqrt{3361}-1}{14}\right)$$

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.

$$7x^{2}+x-120=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 7\left(-120\right)}}{2\times 7}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\times 7\left(-120\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-1±\sqrt{1-28\left(-120\right)}}{2\times 7}$$

Multiply -28 times -120.

$$x=\frac{-1±\sqrt{1+3360}}{2\times 7}$$

Add 1 to 3360.

$$x=\frac{-1±\sqrt{3361}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-1±\sqrt{3361}}{14}$$

Now solve the equation x=\frac{-1±\sqrt{3361}}{14} when ± is plus. Add -1 to \sqrt{3361}.

$$x=\frac{\sqrt{3361}-1}{14}$$

Now solve the equation x=\frac{-1±\sqrt{3361}}{14} when ± is minus. Subtract \sqrt{3361} from -1.

$$x=\frac{-\sqrt{3361}-1}{14}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{3361}}{14} for x_{1} and \frac{-1-\sqrt{3361}}{14} for x_{2}.

$$7x^{2}+x-120=7\left(x-\frac{\sqrt{3361}-1}{14}\right)\left(x-\frac{-\sqrt{3361}-1}{14}\right)$$

Evaluate

$$7x^{2}+x-120$$