Solve 500*100+x/100*100-x/100=1440

$$500 \times \frac { 100 + x } { 100 } \times \frac { 100 - x } { 100 } = 1440$$

Solve for x (complex solution)

$$x=-20\sqrt{47}i\approx -0-137.113092008i$$

$$x=20\sqrt{47}i\approx 137.113092008i$$

Steps by Finding Square Root

Multiply both sides of the equation by 100.

$$500\left(100+x\right)\times \frac{100-x}{100}=144000$$

Cancel out 100, the greatest common factor in 500 and 100.

$$5\left(100-x\right)\left(100+x\right)=144000$$

Use the distributive property to multiply 5\left(100-x\right) by 100+x.

$$50000-500x+5\left(100-x\right)x=144000$$

Use the distributive property to multiply 5 by 100-x.

$$50000-500x+\left(500-5x\right)x=144000$$

Use the distributive property to multiply 500-5x by x.

$$50000-500x+500x-5x^{2}=144000$$

Combine -500x and 500x to get 0.

$$50000-5x^{2}=144000$$

Subtract 50000 from both sides.

$$-5x^{2}=144000-50000$$

Subtract 50000 from 144000 to get 94000.

$$-5x^{2}=94000$$

Divide both sides by -5.

$$x^{2}=\frac{94000}{-5}$$

Divide 94000 by -5 to get -18800.

$$x^{2}=-18800$$

The equation is now solved.

$$x=20\sqrt{47}i x=-20\sqrt{47}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 100.

$$500\left(100+x\right)\times \frac{100-x}{100}=144000$$

Cancel out 100, the greatest common factor in 500 and 100.

$$5\left(100-x\right)\left(100+x\right)=144000$$

Use the distributive property to multiply 5\left(100-x\right) by 100+x.

$$50000-500x+5\left(100-x\right)x=144000$$

Use the distributive property to multiply 5 by 100-x.

$$50000-500x+\left(500-5x\right)x=144000$$

Use the distributive property to multiply 500-5x by x.

$$50000-500x+500x-5x^{2}=144000$$

Combine -500x and 500x to get 0.

$$50000-5x^{2}=144000$$

Subtract 144000 from both sides.

$$50000-5x^{2}-144000=0$$

Subtract 144000 from 50000 to get -94000.

$$-94000-5x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-5x^{2}-94000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and -94000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\left(-94000\right)}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\left(-94000\right)}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\left(-94000\right)}}{2\left(-5\right)}$$

Multiply 20 times -94000.

$$x=\frac{0±\sqrt{-1880000}}{2\left(-5\right)}$$

Take the square root of -1880000.

$$x=\frac{0±200\sqrt{47}i}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±200\sqrt{47}i}{-10}$$

Now solve the equation x=\frac{0±200\sqrt{47}i}{-10} when ± is plus.

$$x=-20\sqrt{47}i$$

Now solve the equation x=\frac{0±200\sqrt{47}i}{-10} when ± is minus.

$$x=20\sqrt{47}i$$

The equation is now solved.

$$x=-20\sqrt{47}i x=20\sqrt{47}i$$