Solve x^2+5x-50*4x-20

$$x ^ { 2 } + 5 x - 50 \cdot 4 x - 20$$

Evaluate

$$x^{2}-195x-20$$

Solution Steps

Multiply 50 and 4 to get 200.

$$x^{2}+5x-200x-20$$

Combine 5x and -200x to get -195x.

$$x^{2}-195x-20$$

Factor

$$\left(x-\frac{195-\sqrt{38105}}{2}\right)\left(x-\frac{\sqrt{38105}+195}{2}\right)$$

Steps Using the Quadratic Formula

Multiply 50 and 4 to get 200.

$$factor(x^{2}+5x-200x-20)$$

Combine 5x and -200x to get -195x.

$$factor(x^{2}-195x-20)$$

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.

$$x^{2}-195x-20=0$$

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.

$$x=\frac{-\left(-195\right)±\sqrt{\left(-195\right)^{2}-4\left(-20\right)}}{2}$$

Square -195.

$$x=\frac{-\left(-195\right)±\sqrt{38025-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$x=\frac{-\left(-195\right)±\sqrt{38025+80}}{2}$$

Add 38025 to 80.

$$x=\frac{-\left(-195\right)±\sqrt{38105}}{2}$$

The opposite of -195 is 195.

$$x=\frac{195±\sqrt{38105}}{2}$$

Now solve the equation x=\frac{195±\sqrt{38105}}{2} when ± is plus. Add 195 to \sqrt{38105}.

$$x=\frac{\sqrt{38105}+195}{2}$$

Now solve the equation x=\frac{195±\sqrt{38105}}{2} when ± is minus. Subtract \sqrt{38105} from 195.

$$x=\frac{195-\sqrt{38105}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{195+\sqrt{38105}}{2} for x_{1} and \frac{195-\sqrt{38105}}{2} for x_{2}.

$$x^{2}-195x-20=\left(x-\frac{\sqrt{38105}+195}{2}\right)\left(x-\frac{195-\sqrt{38105}}{2}\right)$$