Solve x^2-4x-5=25*6

$${ x }^{ 2 } -4x-5 = 25 \times 6$$

Solve for x

$$x=\sqrt{159}+2\approx 14.609520213$$

$$x=2-\sqrt{159}\approx -10.609520213$$

Steps Using the Quadratic Formula

Multiply 25 and 6 to get 150.

$$x^{2}-4x-5=150$$

Subtract 150 from both sides.

$$x^{2}-4x-5-150=0$$

Subtract 150 from -5 to get -155.

$$x^{2}-4x-155=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and -155 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-155\right)}}{2}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-155\right)}}{2}$$

Multiply -4 times -155.

$$x=\frac{-\left(-4\right)±\sqrt{16+620}}{2}$$

Add 16 to 620.

$$x=\frac{-\left(-4\right)±\sqrt{636}}{2}$$

Take the square root of 636.

$$x=\frac{-\left(-4\right)±2\sqrt{159}}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±2\sqrt{159}}{2}$$

Now solve the equation x=\frac{4±2\sqrt{159}}{2} when ± is plus. Add 4 to 2\sqrt{159}.

$$x=\frac{2\sqrt{159}+4}{2}$$

Divide 4+2\sqrt{159} by 2.

$$x=\sqrt{159}+2$$

Now solve the equation x=\frac{4±2\sqrt{159}}{2} when ± is minus. Subtract 2\sqrt{159} from 4.

$$x=\frac{4-2\sqrt{159}}{2}$$

Divide 4-2\sqrt{159} by 2.

$$x=2-\sqrt{159}$$

The equation is now solved.

$$x=\sqrt{159}+2 x=2-\sqrt{159}$$

Steps for Completing the Square

Multiply 25 and 6 to get 150.

$$x^{2}-4x-5=150$$

Add 5 to both sides.

$$x^{2}-4x=150+5$$

Add 150 and 5 to get 155.

$$x^{2}-4x=155$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=155+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=155+4$$

Add 155 to 4.

$$x^{2}-4x+4=159$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=159$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{159}$$

Simplify.

$$x-2=\sqrt{159} x-2=-\sqrt{159}$$

Add 2 to both sides of the equation.

$$x=\sqrt{159}+2 x=2-\sqrt{159}$$