Solve (x^2-35x-30)

$$( x ^ { 2 } - 35 x - 30 )$$

Factor

$$\left(x-\frac{35-\sqrt{1345}}{2}\right)\left(x-\frac{\sqrt{1345}+35}{2}\right)$$

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.

$$x^{2}-35x-30=0$$

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.

$$x=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}-4\left(-30\right)}}{2}$$

Square -35.

$$x=\frac{-\left(-35\right)±\sqrt{1225-4\left(-30\right)}}{2}$$

Multiply -4 times -30.

$$x=\frac{-\left(-35\right)±\sqrt{1225+120}}{2}$$

Add 1225 to 120.

$$x=\frac{-\left(-35\right)±\sqrt{1345}}{2}$$

The opposite of -35 is 35.

$$x=\frac{35±\sqrt{1345}}{2}$$

Now solve the equation x=\frac{35±\sqrt{1345}}{2} when ± is plus. Add 35 to \sqrt{1345}.

$$x=\frac{\sqrt{1345}+35}{2}$$

Now solve the equation x=\frac{35±\sqrt{1345}}{2} when ± is minus. Subtract \sqrt{1345} from 35.

$$x=\frac{35-\sqrt{1345}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{35+\sqrt{1345}}{2} for x_{1} and \frac{35-\sqrt{1345}}{2} for x_{2}.

$$x^{2}-35x-30=\left(x-\frac{\sqrt{1345}+35}{2}\right)\left(x-\frac{35-\sqrt{1345}}{2}\right)$$

Evaluate

$$x^{2}-35x-30$$