Solve 99814000=x^2+200x

$$99814000 = x ^ { 2 } + 200 x$$

Solve for x

$$x=40\sqrt{62390}-100\approx 9891.196124589$$

$$x=-40\sqrt{62390}-100\approx -10091.196124589$$

Steps Using the Quadratic Formula

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

$$x^{2}+200x=99814000$$

Subtract 99814000 from both sides.

$$x^{2}+200x-99814000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 200 for b, and -99814000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-200±\sqrt{200^{2}-4\left(-99814000\right)}}{2}$$

Square 200.

$$x=\frac{-200±\sqrt{40000-4\left(-99814000\right)}}{2}$$

Multiply -4 times -99814000.

$$x=\frac{-200±\sqrt{40000+399256000}}{2}$$

Add 40000 to 399256000.

$$x=\frac{-200±\sqrt{399296000}}{2}$$

Take the square root of 399296000.

$$x=\frac{-200±80\sqrt{62390}}{2}$$

Now solve the equation x=\frac{-200±80\sqrt{62390}}{2} when ± is plus. Add -200 to 80\sqrt{62390}.

$$x=\frac{80\sqrt{62390}-200}{2}$$

Divide -200+80\sqrt{62390} by 2.

$$x=40\sqrt{62390}-100$$

Now solve the equation x=\frac{-200±80\sqrt{62390}}{2} when ± is minus. Subtract 80\sqrt{62390} from -200.

$$x=\frac{-80\sqrt{62390}-200}{2}$$

Divide -200-80\sqrt{62390} by 2.

$$x=-40\sqrt{62390}-100$$

The equation is now solved.

$$x=40\sqrt{62390}-100 x=-40\sqrt{62390}-100$$

Steps for Completing the Square

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

$$x^{2}+200x=99814000$$

Divide 200, the coefficient of the x term, by 2 to get 100. Then add the square of 100 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+200x+100^{2}=99814000+100^{2}$$

Square 100.

$$x^{2}+200x+10000=99814000+10000$$

Add 99814000 to 10000.

$$x^{2}+200x+10000=99824000$$

Factor x^{2}+200x+10000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+100\right)^{2}=99824000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+100\right)^{2}}=\sqrt{99824000}$$

Simplify.

$$x+100=40\sqrt{62390} x+100=-40\sqrt{62390}$$

Subtract 100 from both sides of the equation.

$$x=40\sqrt{62390}-100 x=-40\sqrt{62390}-100$$