Solve x=-1018-9000/x

$$x=-1018- \frac{ 9000 }{ x }$$

Solve for x (complex solution)

$$x=\sqrt{250081}-509\approx -8.91900656$$

$$x=-\left(\sqrt{250081}+509\right)\approx -1009.08099344$$

Steps Using the Quadratic Formula

To add or subtract expressions, expand them to make their denominators the same. Multiply -1018 times \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Since -\frac{1018x}{x} and \frac{9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-1018x-9000}{x}$$

Subtract \frac{-1018x-9000}{x} from both sides.

$$x-\frac{-1018x-9000}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Since \frac{xx}{x} and \frac{-1018x-9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Do the multiplications in xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x^{2}+1018x+9000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1018 for b, and 9000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

Square 1018.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

Multiply -4 times 9000.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

Add 1036324 to -36000.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

Take the square root of 1000324.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

Now solve the equation x=\frac{-1018±2\sqrt{250081}}{2} when ± is plus. Add -1018 to 2\sqrt{250081}.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

Divide -1018+2\sqrt{250081} by 2.

$$x=\sqrt{250081}-509$$

Now solve the equation x=\frac{-1018±2\sqrt{250081}}{2} when ± is minus. Subtract 2\sqrt{250081} from -1018.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

Divide -1018-2\sqrt{250081} by 2.

$$x=-\sqrt{250081}-509$$

The equation is now solved.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Steps for Completing the Square

To add or subtract expressions, expand them to make their denominators the same. Multiply -1018 times \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Since -\frac{1018x}{x} and \frac{9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-1018x-9000}{x}$$

Subtract \frac{-1018x-9000}{x} from both sides.

$$x-\frac{-1018x-9000}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Since \frac{xx}{x} and \frac{-1018x-9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Do the multiplications in xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x^{2}+1018x+9000=0$$

Subtract 9000 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+1018x=-9000$$

Divide 1018, the coefficient of the x term, by 2 to get 509. Then add the square of 509 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

Square 509.

$$x^{2}+1018x+259081=-9000+259081$$

Add -9000 to 259081.

$$x^{2}+1018x+259081=250081$$

Factor x^{2}+1018x+259081. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+509\right)^{2}=250081$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Simplify.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Subtract 509 from both sides of the equation.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Solve for x

$$x=\sqrt{250081}-509\approx -8.91900656$$

$$x=-\sqrt{250081}-509\approx -1009.08099344$$

Steps Using the Quadratic Formula

To add or subtract expressions, expand them to make their denominators the same. Multiply -1018 times \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Since -\frac{1018x}{x} and \frac{9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-1018x-9000}{x}$$

Subtract \frac{-1018x-9000}{x} from both sides.

$$x-\frac{-1018x-9000}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Since \frac{xx}{x} and \frac{-1018x-9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Do the multiplications in xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x^{2}+1018x+9000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1018 for b, and 9000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

Square 1018.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

Multiply -4 times 9000.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

Add 1036324 to -36000.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

Take the square root of 1000324.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

Now solve the equation x=\frac{-1018±2\sqrt{250081}}{2} when ± is plus. Add -1018 to 2\sqrt{250081}.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

Divide -1018+2\sqrt{250081} by 2.

$$x=\sqrt{250081}-509$$

Now solve the equation x=\frac{-1018±2\sqrt{250081}}{2} when ± is minus. Subtract 2\sqrt{250081} from -1018.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

Divide -1018-2\sqrt{250081} by 2.

$$x=-\sqrt{250081}-509$$

The equation is now solved.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Steps for Completing the Square

To add or subtract expressions, expand them to make their denominators the same. Multiply -1018 times \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Since -\frac{1018x}{x} and \frac{9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-1018x-9000}{x}$$

Subtract \frac{-1018x-9000}{x} from both sides.

$$x-\frac{-1018x-9000}{x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Since \frac{xx}{x} and \frac{-1018x-9000}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Do the multiplications in xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x^{2}+1018x+9000=0$$

Subtract 9000 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}+1018x=-9000$$

Divide 1018, the coefficient of the x term, by 2 to get 509. Then add the square of 509 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

Square 509.

$$x^{2}+1018x+259081=-9000+259081$$

Add -9000 to 259081.

$$x^{2}+1018x+259081=250081$$

Factor x^{2}+1018x+259081. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+509\right)^{2}=250081$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Simplify.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Subtract 509 from both sides of the equation.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$