Solve -51x^2-2x^2-154=56

$$-51 { x }^{ 2 } -2 { x }^{ 2 } -154=56$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{11130}i}{53}\approx -0-1.990543682i$$

$$x=\frac{\sqrt{11130}i}{53}\approx 1.990543682i$$

Steps by Finding Square Root

Combine -51x^{2} and -2x^{2} to get -53x^{2}.

$$-53x^{2}-154=56$$

Add 154 to both sides.

$$-53x^{2}=56+154$$

Add 56 and 154 to get 210.

$$-53x^{2}=210$$

Divide both sides by -53.

$$x^{2}=-\frac{210}{53}$$

The equation is now solved.

$$x=\frac{\sqrt{11130}i}{53} x=-\frac{\sqrt{11130}i}{53}$$

Steps Using the Quadratic Formula

Combine -51x^{2} and -2x^{2} to get -53x^{2}.

$$-53x^{2}-154=56$$

Subtract 56 from both sides.

$$-53x^{2}-154-56=0$$

Subtract 56 from -154 to get -210.

$$-53x^{2}-210=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -53 for a, 0 for b, and -210 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-53\right)\left(-210\right)}}{2\left(-53\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-53\right)\left(-210\right)}}{2\left(-53\right)}$$

Multiply -4 times -53.

$$x=\frac{0±\sqrt{212\left(-210\right)}}{2\left(-53\right)}$$

Multiply 212 times -210.

$$x=\frac{0±\sqrt{-44520}}{2\left(-53\right)}$$

Take the square root of -44520.

$$x=\frac{0±2\sqrt{11130}i}{2\left(-53\right)}$$

Multiply 2 times -53.

$$x=\frac{0±2\sqrt{11130}i}{-106}$$

Now solve the equation x=\frac{0±2\sqrt{11130}i}{-106} when ± is plus.

$$x=-\frac{\sqrt{11130}i}{53}$$

Now solve the equation x=\frac{0±2\sqrt{11130}i}{-106} when ± is minus.

$$x=\frac{\sqrt{11130}i}{53}$$

The equation is now solved.

$$x=-\frac{\sqrt{11130}i}{53} x=\frac{\sqrt{11130}i}{53}$$