Solve 0=xleft(200+10(150-x)right)

$$0 = x \left( 200+10(150-x) \right)$$

Solve for x

$$x=170$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 10 by 150-x.

$$0=x\left(200+1500-10x\right)$$

Add 200 and 1500 to get 1700.

$$0=x\left(1700-10x\right)$$

Use the distributive property to multiply x by 1700-10x.

$$0=1700x-10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1700x-10x^{2}=0$$

Factor out x.

$$x\left(1700-10x\right)=0$$

To find equation solutions, solve x=0 and 1700-10x=0.

$$x=0 x=170$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 10 by 150-x.

$$0=x\left(200+1500-10x\right)$$

Add 200 and 1500 to get 1700.

$$0=x\left(1700-10x\right)$$

Use the distributive property to multiply x by 1700-10x.

$$0=1700x-10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1700x-10x^{2}=0$$

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.

$$-10x^{2}+1700x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10 for a, 1700 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1700±\sqrt{1700^{2}}}{2\left(-10\right)}$$

Take the square root of 1700^{2}.

$$x=\frac{-1700±1700}{2\left(-10\right)}$$

Multiply 2 times -10.

$$x=\frac{-1700±1700}{-20}$$

Now solve the equation x=\frac{-1700±1700}{-20} when ± is plus. Add -1700 to 1700.

$$x=\frac{0}{-20}$$

Divide 0 by -20.

$$x=0$$

Now solve the equation x=\frac{-1700±1700}{-20} when ± is minus. Subtract 1700 from -1700.

$$x=-\frac{3400}{-20}$$

Divide -3400 by -20.

$$x=170$$

The equation is now solved.

$$x=0 x=170$$

Steps for Completing the Square

Use the distributive property to multiply 10 by 150-x.

$$0=x\left(200+1500-10x\right)$$

Add 200 and 1500 to get 1700.

$$0=x\left(1700-10x\right)$$

Use the distributive property to multiply x by 1700-10x.

$$0=1700x-10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1700x-10x^{2}=0$$

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.

$$-10x^{2}+1700x=0$$

Divide both sides by -10.

$$\frac{-10x^{2}+1700x}{-10}=\frac{0}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$x^{2}+\frac{1700}{-10}x=\frac{0}{-10}$$

Divide 1700 by -10.

$$x^{2}-170x=\frac{0}{-10}$$

Divide 0 by -10.

$$x^{2}-170x=0$$

Divide -170, the coefficient of the x term, by 2 to get -85. Then add the square of -85 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-170x+\left(-85\right)^{2}=\left(-85\right)^{2}$$

Square -85.

$$x^{2}-170x+7225=7225$$

Factor x^{2}-170x+7225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-85\right)^{2}=7225$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-85\right)^{2}}=\sqrt{7225}$$

Simplify.

$$x-85=85 x-85=-85$$

Add 85 to both sides of the equation.

$$x=170 x=0$$