Solve 450=((x+20)div150)*x

$$450=((x+20) \div 150) \times x$$

Solve for x

$$x=-270$$

$$x=250$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 150.

$$67500=\left(x+20\right)x$$

Use the distributive property to multiply x+20 by x.

$$67500=x^{2}+20x$$

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

$$x^{2}+20x=67500$$

Subtract 67500 from both sides.

$$x^{2}+20x-67500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 20 for b, and -67500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-67500\right)}}{2}$$

Square 20.

$$x=\frac{-20±\sqrt{400-4\left(-67500\right)}}{2}$$

Multiply -4 times -67500.

$$x=\frac{-20±\sqrt{400+270000}}{2}$$

Add 400 to 270000.

$$x=\frac{-20±\sqrt{270400}}{2}$$

Take the square root of 270400.

$$x=\frac{-20±520}{2}$$

Now solve the equation x=\frac{-20±520}{2} when ± is plus. Add -20 to 520.

$$x=\frac{500}{2}$$

Divide 500 by 2.

$$x=250$$

Now solve the equation x=\frac{-20±520}{2} when ± is minus. Subtract 520 from -20.

$$x=-\frac{540}{2}$$

Divide -540 by 2.

$$x=-270$$

The equation is now solved.

$$x=250 x=-270$$

Steps for Completing the Square

Multiply both sides of the equation by 150.

$$67500=\left(x+20\right)x$$

Use the distributive property to multiply x+20 by x.

$$67500=x^{2}+20x$$

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

$$x^{2}+20x=67500$$

Divide 20, the coefficient of the x term, by 2 to get 10. Then add the square of 10 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+20x+10^{2}=67500+10^{2}$$

Square 10.

$$x^{2}+20x+100=67500+100$$

Add 67500 to 100.

$$x^{2}+20x+100=67600$$

Factor x^{2}+20x+100. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+10\right)^{2}=67600$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{67600}$$

Simplify.

$$x+10=260 x+10=-260$$

Subtract 10 from both sides of the equation.

$$x=250 x=-270$$