Solve x^2-24(x^2)-25=0

$${ x }^{ 2 } -24( { x }^{ 2 } )-25=0$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{23}i}{23}\approx -0-1.04257207i$$

$$x=\frac{5\sqrt{23}i}{23}\approx 1.04257207i$$

Steps by Finding Square Root

Combine x^{2} and -24x^{2} to get -23x^{2}.

$$-23x^{2}-25=0$$

Add 25 to both sides. Anything plus zero gives itself.

$$-23x^{2}=25$$

Divide both sides by -23.

$$x^{2}=-\frac{25}{23}$$

The equation is now solved.

$$x=\frac{5\sqrt{23}i}{23} x=-\frac{5\sqrt{23}i}{23}$$

Steps Using the Quadratic Formula

Combine x^{2} and -24x^{2} to get -23x^{2}.

$$-23x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -23 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-23\right)\left(-25\right)}}{2\left(-23\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-23\right)\left(-25\right)}}{2\left(-23\right)}$$

Multiply -4 times -23.

$$x=\frac{0±\sqrt{92\left(-25\right)}}{2\left(-23\right)}$$

Multiply 92 times -25.

$$x=\frac{0±\sqrt{-2300}}{2\left(-23\right)}$$

Take the square root of -2300.

$$x=\frac{0±10\sqrt{23}i}{2\left(-23\right)}$$

Multiply 2 times -23.

$$x=\frac{0±10\sqrt{23}i}{-46}$$

Now solve the equation x=\frac{0±10\sqrt{23}i}{-46} when ± is plus.

$$x=-\frac{5\sqrt{23}i}{23}$$

Now solve the equation x=\frac{0±10\sqrt{23}i}{-46} when ± is minus.

$$x=\frac{5\sqrt{23}i}{23}$$

The equation is now solved.

$$x=-\frac{5\sqrt{23}i}{23} x=\frac{5\sqrt{23}i}{23}$$