Solve 2591-x(1-1-15x)=140

$$2591 - x ( 1 - 1 - 15 x ) = 140$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{4085}i}{5}\approx -0-12.782800945i$$

$$x=\frac{\sqrt{4085}i}{5}\approx 12.782800945i$$

Steps by Finding Square Root

Subtract 1 from 1 to get 0.

$$2591-x\left(-15\right)x=140$$

Multiply x and x to get x^{2}.

$$2591-x^{2}\left(-15\right)=140$$

Multiply -1 and -15 to get 15.

$$2591+15x^{2}=140$$

Subtract 2591 from both sides.

$$15x^{2}=140-2591$$

Subtract 2591 from 140 to get -2451.

$$15x^{2}=-2451$$

Divide both sides by 15.

$$x^{2}=\frac{-2451}{15}$$

Reduce the fraction \frac{-2451}{15} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{817}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{4085}i}{5} x=-\frac{\sqrt{4085}i}{5}$$

Steps Using the Quadratic Formula

Subtract 1 from 1 to get 0.

$$2591-x\left(-15\right)x=140$$

Multiply x and x to get x^{2}.

$$2591-x^{2}\left(-15\right)=140$$

Subtract 140 from both sides.

$$2591-x^{2}\left(-15\right)-140=0$$

Multiply -1 and -15 to get 15.

$$2591+15x^{2}-140=0$$

Subtract 140 from 2591 to get 2451.

$$2451+15x^{2}=0$$

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.

$$15x^{2}+2451=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and 2451 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15\times 2451}}{2\times 15}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15\times 2451}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60\times 2451}}{2\times 15}$$

Multiply -60 times 2451.

$$x=\frac{0±\sqrt{-147060}}{2\times 15}$$

Take the square root of -147060.

$$x=\frac{0±6\sqrt{4085}i}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{0±6\sqrt{4085}i}{30}$$

Now solve the equation x=\frac{0±6\sqrt{4085}i}{30} when ± is plus.

$$x=\frac{\sqrt{4085}i}{5}$$

Now solve the equation x=\frac{0±6\sqrt{4085}i}{30} when ± is minus.

$$x=-\frac{\sqrt{4085}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{4085}i}{5} x=-\frac{\sqrt{4085}i}{5}$$