Solve 70x-300+x^2

$$70 x - 300 + x ^ { 2 }$$

Factor

$$\left(x-\left(-5\sqrt{61}-35\right)\right)\left(x-\left(5\sqrt{61}-35\right)\right)$$

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.

$$x^{2}+70x-300=0$$

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.

$$x=\frac{-70±\sqrt{70^{2}-4\left(-300\right)}}{2}$$

Square 70.

$$x=\frac{-70±\sqrt{4900-4\left(-300\right)}}{2}$$

Multiply -4 times -300.

$$x=\frac{-70±\sqrt{4900+1200}}{2}$$

Add 4900 to 1200.

$$x=\frac{-70±\sqrt{6100}}{2}$$

Take the square root of 6100.

$$x=\frac{-70±10\sqrt{61}}{2}$$

Now solve the equation x=\frac{-70±10\sqrt{61}}{2} when ± is plus. Add -70 to 10\sqrt{61}.

$$x=\frac{10\sqrt{61}-70}{2}$$

Divide -70+10\sqrt{61} by 2.

$$x=5\sqrt{61}-35$$

Now solve the equation x=\frac{-70±10\sqrt{61}}{2} when ± is minus. Subtract 10\sqrt{61} from -70.

$$x=\frac{-10\sqrt{61}-70}{2}$$

Divide -70-10\sqrt{61} by 2.

$$x=-5\sqrt{61}-35$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -35+5\sqrt{61} for x_{1} and -35-5\sqrt{61} for x_{2}.

$$x^{2}+70x-300=\left(x-\left(5\sqrt{61}-35\right)\right)\left(x-\left(-5\sqrt{61}-35\right)\right)$$

Evaluate

$$x^{2}+70x-300$$