Solve 440(x+8)-440x/x(x+8)=1/2

$$\frac { 440 ( x + 8 ) - 440 x } { x ( x + 8 ) } = \frac { 1 } { 2 }$$

Solve for x

$$x=-88$$

$$x=80$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -8,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+8\right), the least common multiple of x\left(x+8\right),2.

$$2\left(440\left(x+8\right)-440x\right)=x\left(x+8\right)$$

Use the distributive property to multiply 440 by x+8.

$$2\left(440x+3520-440x\right)=x\left(x+8\right)$$

Combine 440x and -440x to get 0.

$$2\times 3520=x\left(x+8\right)$$

Multiply 2 and 3520 to get 7040.

$$7040=x\left(x+8\right)$$

Use the distributive property to multiply x by x+8.

$$7040=x^{2}+8x$$

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

$$x^{2}+8x=7040$$

Subtract 7040 from both sides.

$$x^{2}+8x-7040=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -7040 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-7040\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-7040\right)}}{2}$$

Multiply -4 times -7040.

$$x=\frac{-8±\sqrt{64+28160}}{2}$$

Add 64 to 28160.

$$x=\frac{-8±\sqrt{28224}}{2}$$

Take the square root of 28224.

$$x=\frac{-8±168}{2}$$

Now solve the equation x=\frac{-8±168}{2} when ± is plus. Add -8 to 168.

$$x=\frac{160}{2}$$

Divide 160 by 2.

$$x=80$$

Now solve the equation x=\frac{-8±168}{2} when ± is minus. Subtract 168 from -8.

$$x=-\frac{176}{2}$$

Divide -176 by 2.

$$x=-88$$

The equation is now solved.

$$x=80 x=-88$$

Steps for Completing the Square

Variable x cannot be equal to any of the values -8,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+8\right), the least common multiple of x\left(x+8\right),2.

$$2\left(440\left(x+8\right)-440x\right)=x\left(x+8\right)$$

Use the distributive property to multiply 440 by x+8.

$$2\left(440x+3520-440x\right)=x\left(x+8\right)$$

Combine 440x and -440x to get 0.

$$2\times 3520=x\left(x+8\right)$$

Multiply 2 and 3520 to get 7040.

$$7040=x\left(x+8\right)$$

Use the distributive property to multiply x by x+8.

$$7040=x^{2}+8x$$

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

$$x^{2}+8x=7040$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=7040+4^{2}$$

Square 4.

$$x^{2}+8x+16=7040+16$$

Add 7040 to 16.

$$x^{2}+8x+16=7056$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=7056$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{7056}$$

Simplify.

$$x+4=84 x+4=-84$$

Subtract 4 from both sides of the equation.

$$x=80 x=-88$$