Solve 2(x-6)^2=50

$$2 ( x - 6 ) ^ { 2 } = 50$$

Solve for x

$$x=11$$

$$x=1$$

Steps Using Factoring

Divide both sides by 2.

$$\left(x-6\right)^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$\left(x-6\right)^{2}=25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+36=25$$

Subtract 25 from both sides.

$$x^{2}-12x+36-25=0$$

Subtract 25 from 36 to get 11.

$$x^{2}-12x+11=0$$

To solve the equation, factor x^{2}-12x+11 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.

$$a+b=-12 ab=11$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-11 b=-1$$

Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.

$$\left(x-11\right)\left(x-1\right)$$

To find equation solutions, solve x-11=0 and x-1=0.

$$x=11 x=1$$

Steps Using Factoring By Grouping

Divide both sides by 2.

$$\left(x-6\right)^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$\left(x-6\right)^{2}=25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+36=25$$

Subtract 25 from both sides.

$$x^{2}-12x+36-25=0$$

Subtract 25 from 36 to get 11.

$$x^{2}-12x+11=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx+11. To find a and b, set up a system to be solved.

$$a+b=-12 ab=1\times 11=11$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-11 b=-1$$

Rewrite x^{2}-12x+11 as \left(x^{2}-11x\right)+\left(-x+11\right).

$$\left(x^{2}-11x\right)+\left(-x+11\right)$$

Factor out x in the first and -1 in the second group.

$$x\left(x-11\right)-\left(x-11\right)$$

Factor out common term x-11 by using distributive property.

$$\left(x-11\right)\left(x-1\right)$$

To find equation solutions, solve x-11=0 and x-1=0.

$$x=11 x=1$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$\left(x-6\right)^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$\left(x-6\right)^{2}=25$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+36=25$$

Subtract 25 from both sides.

$$x^{2}-12x+36-25=0$$

Subtract 25 from 36 to get 11.

$$x^{2}-12x+11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -12 for b, and 11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 11}}{2}$$

Square -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 11}}{2}$$

Multiply -4 times 11.

$$x=\frac{-\left(-12\right)±\sqrt{144-44}}{2}$$

Add 144 to -44.

$$x=\frac{-\left(-12\right)±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{-\left(-12\right)±10}{2}$$

The opposite of -12 is 12.

$$x=\frac{12±10}{2}$$

Now solve the equation x=\frac{12±10}{2} when ± is plus. Add 12 to 10.

$$x=\frac{22}{2}$$

Divide 22 by 2.

$$x=11$$

Now solve the equation x=\frac{12±10}{2} when ± is minus. Subtract 10 from 12.

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

Divide 2 by 2.

$$x=1$$

The equation is now solved.

$$x=11 x=1$$

Steps for Completing the Square

Divide both sides by 2.

$$\left(x-6\right)^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$\left(x-6\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{25}$$

Simplify.

$$x-6=5 x-6=-5$$

Add 6 to both sides of the equation.

$$x=11 x=1$$