Solve x*(-20x+9x)=3100

$$x \cdot ( - 20 x + 9 x ) = 3100$$

Solve for x (complex solution)

$$x=-\frac{10\sqrt{341}i}{11}\approx -0-16.787441193i$$

$$x=\frac{10\sqrt{341}i}{11}\approx 16.787441193i$$

Steps by Finding Square Root

Combine -20x and 9x to get -11x.

$$x\left(-11\right)x=3100$$

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

$$x^{2}\left(-11\right)=3100$$

Divide both sides by -11.

$$x^{2}=-\frac{3100}{11}$$

The equation is now solved.

$$x=\frac{10\sqrt{341}i}{11} x=-\frac{10\sqrt{341}i}{11}$$

Steps Using the Quadratic Formula

Combine -20x and 9x to get -11x.

$$x\left(-11\right)x=3100$$

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

$$x^{2}\left(-11\right)=3100$$

Subtract 3100 from both sides.

$$x^{2}\left(-11\right)-3100=0$$

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.

$$-11x^{2}-3100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -11 for a, 0 for b, and -3100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11\right)\left(-3100\right)}}{2\left(-11\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-11\right)\left(-3100\right)}}{2\left(-11\right)}$$

Multiply -4 times -11.

$$x=\frac{0±\sqrt{44\left(-3100\right)}}{2\left(-11\right)}$$

Multiply 44 times -3100.

$$x=\frac{0±\sqrt{-136400}}{2\left(-11\right)}$$

Take the square root of -136400.

$$x=\frac{0±20\sqrt{341}i}{2\left(-11\right)}$$

Multiply 2 times -11.

$$x=\frac{0±20\sqrt{341}i}{-22}$$

Now solve the equation x=\frac{0±20\sqrt{341}i}{-22} when ± is plus.

$$x=-\frac{10\sqrt{341}i}{11}$$

Now solve the equation x=\frac{0±20\sqrt{341}i}{-22} when ± is minus.

$$x=\frac{10\sqrt{341}i}{11}$$

The equation is now solved.

$$x=-\frac{10\sqrt{341}i}{11} x=\frac{10\sqrt{341}i}{11}$$