Solve 26x^2+58x-36

$$26 { x }^{ 2 } +58x-36$$

Factor

$$26\left(x-\frac{-\sqrt{1777}-29}{26}\right)\left(x-\frac{\sqrt{1777}-29}{26}\right)$$

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.

$$26x^{2}+58x-36=0$$

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.

$$x=\frac{-58±\sqrt{58^{2}-4\times 26\left(-36\right)}}{2\times 26}$$

Square 58.

$$x=\frac{-58±\sqrt{3364-4\times 26\left(-36\right)}}{2\times 26}$$

Multiply -4 times 26.

$$x=\frac{-58±\sqrt{3364-104\left(-36\right)}}{2\times 26}$$

Multiply -104 times -36.

$$x=\frac{-58±\sqrt{3364+3744}}{2\times 26}$$

Add 3364 to 3744.

$$x=\frac{-58±\sqrt{7108}}{2\times 26}$$

Take the square root of 7108.

$$x=\frac{-58±2\sqrt{1777}}{2\times 26}$$

Multiply 2 times 26.

$$x=\frac{-58±2\sqrt{1777}}{52}$$

Now solve the equation x=\frac{-58±2\sqrt{1777}}{52} when ± is plus. Add -58 to 2\sqrt{1777}.

$$x=\frac{2\sqrt{1777}-58}{52}$$

Divide -58+2\sqrt{1777} by 52.

$$x=\frac{\sqrt{1777}-29}{26}$$

Now solve the equation x=\frac{-58±2\sqrt{1777}}{52} when ± is minus. Subtract 2\sqrt{1777} from -58.

$$x=\frac{-2\sqrt{1777}-58}{52}$$

Divide -58-2\sqrt{1777} by 52.

$$x=\frac{-\sqrt{1777}-29}{26}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-29+\sqrt{1777}}{26} for x_{1} and \frac{-29-\sqrt{1777}}{26} for x_{2}.

$$26x^{2}+58x-36=26\left(x-\frac{\sqrt{1777}-29}{26}\right)\left(x-\frac{-\sqrt{1777}-29}{26}\right)$$

Evaluate

$$26x^{2}+58x-36$$