Solve x+x(x-1)=2550

$$x+x(x-1)=2550$$

Solve for x

$$x=5\sqrt{102}\approx 50.497524692$$

$$x=-5\sqrt{102}\approx -50.497524692$$

Steps by Finding Square Root

Use the distributive property to multiply x by x-1.

$$x+x^{2}-x=2550$$

Combine x and -x to get 0.

$$x^{2}=2550$$

Take the square root of both sides of the equation.

$$x=5\sqrt{102} x=-5\sqrt{102}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x-1.

$$x+x^{2}-x=2550$$

Combine x and -x to get 0.

$$x^{2}=2550$$

Subtract 2550 from both sides.

$$x^{2}-2550=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2550 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2550\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2550\right)}}{2}$$

Multiply -4 times -2550.

$$x=\frac{0±\sqrt{10200}}{2}$$

Take the square root of 10200.

$$x=\frac{0±10\sqrt{102}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{102}}{2} when ± is plus.

$$x=5\sqrt{102}$$

Now solve the equation x=\frac{0±10\sqrt{102}}{2} when ± is minus.

$$x=-5\sqrt{102}$$

The equation is now solved.

$$x=5\sqrt{102} x=-5\sqrt{102}$$