Solve left(118-xright)^2=08x

$${ \left(118-x \right) }^{ 2 } =08x$$

Solve for x

$$x=118$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(118-x\right)^{2}.

$$13924-236x+x^{2}=0\times 8x$$

Multiply 0 and 8 to get 0.

$$13924-236x+x^{2}=0x$$

Anything times zero gives zero.

$$13924-236x+x^{2}=0$$

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.

$$x^{2}-236x+13924=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -236 for b, and 13924 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-236\right)±\sqrt{\left(-236\right)^{2}-4\times 13924}}{2}$$

Square -236.

$$x=\frac{-\left(-236\right)±\sqrt{55696-4\times 13924}}{2}$$

Multiply -4 times 13924.

$$x=\frac{-\left(-236\right)±\sqrt{55696-55696}}{2}$$

Add 55696 to -55696.

$$x=\frac{-\left(-236\right)±\sqrt{0}}{2}$$

Take the square root of 0.

$$x=-\frac{-236}{2}$$

The opposite of -236 is 236.

$$x=\frac{236}{2}$$

Divide 236 by 2.

$$x=118$$

Steps for Completing the Square

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(118-x\right)^{2}.

$$13924-236x+x^{2}=0\times 8x$$

Multiply 0 and 8 to get 0.

$$13924-236x+x^{2}=0x$$

Anything times zero gives zero.

$$13924-236x+x^{2}=0$$

Subtract 13924 from both sides. Anything subtracted from zero gives its negation.

$$-236x+x^{2}=-13924$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}-236x=-13924$$

Divide -236, the coefficient of the x term, by 2 to get -118. Then add the square of -118 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-236x+\left(-118\right)^{2}=-13924+\left(-118\right)^{2}$$

Square -118.

$$x^{2}-236x+13924=-13924+13924$$

Add -13924 to 13924.

$$x^{2}-236x+13924=0$$

Factor x^{2}-236x+13924. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-118\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-118\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-118=0 x-118=0$$

Add 118 to both sides of the equation.

$$x=118 x=118$$

The equation is now solved. Solutions are the same.

$$x=118$$