Solve x^2+1*80x-5*40=0

$$x ^ { 2 } + 1 \cdot 80 x - 5 \cdot 40 = 0$$

Solve for x

$$x=30\sqrt{2}-40\approx 2.426406871$$

$$x=-30\sqrt{2}-40\approx -82.426406871$$

Steps Using the Quadratic Formula

Multiply 1 and 80 to get 80.

$$x^{2}+80x-5\times 40=0$$

Multiply 5 and 40 to get 200.

$$x^{2}+80x-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 80 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-80±\sqrt{80^{2}-4\left(-200\right)}}{2}$$

Square 80.

$$x=\frac{-80±\sqrt{6400-4\left(-200\right)}}{2}$$

Multiply -4 times -200.

$$x=\frac{-80±\sqrt{6400+800}}{2}$$

Add 6400 to 800.

$$x=\frac{-80±\sqrt{7200}}{2}$$

Take the square root of 7200.

$$x=\frac{-80±60\sqrt{2}}{2}$$

Now solve the equation x=\frac{-80±60\sqrt{2}}{2} when ± is plus. Add -80 to 60\sqrt{2}.

$$x=\frac{60\sqrt{2}-80}{2}$$

Divide -80+60\sqrt{2} by 2.

$$x=30\sqrt{2}-40$$

Now solve the equation x=\frac{-80±60\sqrt{2}}{2} when ± is minus. Subtract 60\sqrt{2} from -80.

$$x=\frac{-60\sqrt{2}-80}{2}$$

Divide -80-60\sqrt{2} by 2.

$$x=-30\sqrt{2}-40$$

The equation is now solved.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$

Steps for Completing the Square

Multiply 1 and 80 to get 80.

$$x^{2}+80x-5\times 40=0$$

Multiply 5 and 40 to get 200.

$$x^{2}+80x-200=0$$

Add 200 to both sides. Anything plus zero gives itself.

$$x^{2}+80x=200$$

Divide 80, the coefficient of the x term, by 2 to get 40. Then add the square of 40 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+80x+40^{2}=200+40^{2}$$

Square 40.

$$x^{2}+80x+1600=200+1600$$

Add 200 to 1600.

$$x^{2}+80x+1600=1800$$

Factor x^{2}+80x+1600. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+40\right)^{2}=1800$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{1800}$$

Simplify.

$$x+40=30\sqrt{2} x+40=-30\sqrt{2}$$

Subtract 40 from both sides of the equation.

$$x=30\sqrt{2}-40 x=-30\sqrt{2}-40$$