Solve 2x^2+58x-357

$$2 { x }^{ 2 } +58x-357$$

Factor

$$2\left(x-\frac{-\sqrt{1555}-29}{2}\right)\left(x-\frac{\sqrt{1555}-29}{2}\right)$$

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.

$$2x^{2}+58x-357=0$$

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.

$$x=\frac{-58±\sqrt{58^{2}-4\times 2\left(-357\right)}}{2\times 2}$$

Square 58.

$$x=\frac{-58±\sqrt{3364-4\times 2\left(-357\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-58±\sqrt{3364-8\left(-357\right)}}{2\times 2}$$

Multiply -8 times -357.

$$x=\frac{-58±\sqrt{3364+2856}}{2\times 2}$$

Add 3364 to 2856.

$$x=\frac{-58±\sqrt{6220}}{2\times 2}$$

Take the square root of 6220.

$$x=\frac{-58±2\sqrt{1555}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-58±2\sqrt{1555}}{4}$$

Now solve the equation x=\frac{-58±2\sqrt{1555}}{4} when ± is plus. Add -58 to 2\sqrt{1555}.

$$x=\frac{2\sqrt{1555}-58}{4}$$

Divide -58+2\sqrt{1555} by 4.

$$x=\frac{\sqrt{1555}-29}{2}$$

Now solve the equation x=\frac{-58±2\sqrt{1555}}{4} when ± is minus. Subtract 2\sqrt{1555} from -58.

$$x=\frac{-2\sqrt{1555}-58}{4}$$

Divide -58-2\sqrt{1555} by 4.

$$x=\frac{-\sqrt{1555}-29}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-29+\sqrt{1555}}{2} for x_{1} and \frac{-29-\sqrt{1555}}{2} for x_{2}.

$$2x^{2}+58x-357=2\left(x-\frac{\sqrt{1555}-29}{2}\right)\left(x-\frac{-\sqrt{1555}-29}{2}\right)$$

Evaluate

$$2x^{2}+58x-357$$