Solve 4x^2-115x-375=

$$4 { x }^{ 2 } -115x-375=$$

Factor

$$4\left(x-\frac{115-5\sqrt{769}}{8}\right)\left(x-\frac{5\sqrt{769}+115}{8}\right)$$

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.

$$4x^{2}-115x-375=0$$

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.

$$x=\frac{-\left(-115\right)±\sqrt{\left(-115\right)^{2}-4\times 4\left(-375\right)}}{2\times 4}$$

Square -115.

$$x=\frac{-\left(-115\right)±\sqrt{13225-4\times 4\left(-375\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\left(-115\right)±\sqrt{13225-16\left(-375\right)}}{2\times 4}$$

Multiply -16 times -375.

$$x=\frac{-\left(-115\right)±\sqrt{13225+6000}}{2\times 4}$$

Add 13225 to 6000.

$$x=\frac{-\left(-115\right)±\sqrt{19225}}{2\times 4}$$

Take the square root of 19225.

$$x=\frac{-\left(-115\right)±5\sqrt{769}}{2\times 4}$$

The opposite of -115 is 115.

$$x=\frac{115±5\sqrt{769}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{115±5\sqrt{769}}{8}$$

Now solve the equation x=\frac{115±5\sqrt{769}}{8} when ± is plus. Add 115 to 5\sqrt{769}.

$$x=\frac{5\sqrt{769}+115}{8}$$

Now solve the equation x=\frac{115±5\sqrt{769}}{8} when ± is minus. Subtract 5\sqrt{769} from 115.

$$x=\frac{115-5\sqrt{769}}{8}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{115+5\sqrt{769}}{8} for x_{1} and \frac{115-5\sqrt{769}}{8} for x_{2}.

$$4x^{2}-115x-375=4\left(x-\frac{5\sqrt{769}+115}{8}\right)\left(x-\frac{115-5\sqrt{769}}{8}\right)$$

Evaluate

$$4x^{2}-115x-375$$