Solve 360*5/x(x+5)=1

$$\frac { 360 \times 5 } { x ( x + 5 ) } = 1$$

Solve for x

$$x=-45$$

$$x=40$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right).

$$360\times 5=x\left(x+5\right)$$

Multiply 360 and 5 to get 1800.

$$1800=x\left(x+5\right)$$

Use the distributive property to multiply x by x+5.

$$1800=x^{2}+5x$$

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

$$x^{2}+5x=1800$$

Subtract 1800 from both sides.

$$x^{2}+5x-1800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 5 for b, and -1800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-1800\right)}}{2}$$

Square 5.

$$x=\frac{-5±\sqrt{25-4\left(-1800\right)}}{2}$$

Multiply -4 times -1800.

$$x=\frac{-5±\sqrt{25+7200}}{2}$$

Add 25 to 7200.

$$x=\frac{-5±\sqrt{7225}}{2}$$

Take the square root of 7225.

$$x=\frac{-5±85}{2}$$

Now solve the equation x=\frac{-5±85}{2} when ± is plus. Add -5 to 85.

$$x=\frac{80}{2}$$

Divide 80 by 2.

$$x=40$$

Now solve the equation x=\frac{-5±85}{2} when ± is minus. Subtract 85 from -5.

$$x=-\frac{90}{2}$$

Divide -90 by 2.

$$x=-45$$

The equation is now solved.

$$x=40 x=-45$$

Steps for Completing the Square

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right).

$$360\times 5=x\left(x+5\right)$$

Multiply 360 and 5 to get 1800.

$$1800=x\left(x+5\right)$$

Use the distributive property to multiply x by x+5.

$$1800=x^{2}+5x$$

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

$$x^{2}+5x=1800$$

Divide 5, the coefficient of the x term, by 2 to get \frac{5}{2}. Then add the square of \frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=1800+\left(\frac{5}{2}\right)^{2}$$

Square \frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+5x+\frac{25}{4}=1800+\frac{25}{4}$$

Add 1800 to \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{7225}{4}$$

Factor x^{2}+5x+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{7225}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{7225}{4}}$$

Simplify.

$$x+\frac{5}{2}=\frac{85}{2} x+\frac{5}{2}=-\frac{85}{2}$$

Subtract \frac{5}{2} from both sides of the equation.

$$x=40 x=-45$$