Solve 50+x^2-10x=50

$$50 + x ^ { 2 } - 10 x = 50$$

Solve for x

$$x=10$$

$$x=0$$

Steps Using Factoring

Subtract 50 from both sides.

$$50+x^{2}-10x-50=0$$

Subtract 50 from 50 to get 0.

$$x^{2}-10x=0$$

Factor out x.

$$x\left(x-10\right)=0$$

To find equation solutions, solve x=0 and x-10=0.

$$x=0 x=10$$

Steps Using the Quadratic Formula

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.

$$x^{2}-10x+50=50$$

Subtract 50 from both sides of the equation.

$$x^{2}-10x+50-50=50-50$$

Subtracting 50 from itself leaves 0.

$$x^{2}-10x+50-50=0$$

Subtract 50 from 50.

$$x^{2}-10x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2}$$

Take the square root of \left(-10\right)^{2}.

$$x=\frac{-\left(-10\right)±10}{2}$$

The opposite of -10 is 10.

$$x=\frac{10±10}{2}$$

Now solve the equation x=\frac{10±10}{2} when ± is plus. Add 10 to 10.

$$x=\frac{20}{2}$$

Divide 20 by 2.

$$x=10$$

Now solve the equation x=\frac{10±10}{2} when ± is minus. Subtract 10 from 10.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=10 x=0$$

Steps for Completing the Square

Subtract 50 from both sides.

$$50+x^{2}-10x-50=0$$

Subtract 50 from 50 to get 0.

$$x^{2}-10x=0$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-10x+\left(-5\right)^{2}=\left(-5\right)^{2}$$

Square -5.

$$x^{2}-10x+25=25$$

Factor x^{2}-10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-5\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{25}$$

Simplify.

$$x-5=5 x-5=-5$$

Add 5 to both sides of the equation.

$$x=10 x=0$$