Solve 15-4*e^{2}*x^2=25x^2+4(4x^2-25x^2)

$$15 - 4 \cdot e ^ { 2 } \cdot x ^ { 2 } = 25 x ^ { 2 } + 4 ( 4 x ^ { 2 } - 25 x ^ { 2 } )$$

Solve for x (complex solution)

$$x=-i\sqrt{\frac{15}{-4e^{2}+59}}\approx -0-0.713754534i$$

$$x=i\sqrt{\frac{15}{-4e^{2}+59}}\approx 0.713754534i$$

Steps by Finding Square Root

Combine 4x^{2} and -25x^{2} to get -21x^{2}.

$$15-4e^{2}x^{2}=25x^{2}+4\left(-21\right)x^{2}$$

Multiply 4 and -21 to get -84.

$$15-4e^{2}x^{2}=25x^{2}-84x^{2}$$

Combine 25x^{2} and -84x^{2} to get -59x^{2}.

$$15-4e^{2}x^{2}=-59x^{2}$$

Add 59x^{2} to both sides.

$$15-4e^{2}x^{2}+59x^{2}=0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$-4e^{2}x^{2}+59x^{2}=-15$$

Combine all terms containing x.

$$\left(-4e^{2}+59\right)x^{2}=-15$$

Dividing by -4e^{2}+59 undoes the multiplication by -4e^{2}+59.

$$x^{2}=-\frac{15}{-4e^{2}+59}$$

Take the square root of both sides of the equation.

$$x=\frac{15i}{\sqrt{-60e^{2}+885}} x=-\frac{15i}{\sqrt{-60e^{2}+885}}$$

The equation is now solved.

$$x=\frac{15i}{\sqrt{-60e^{2}+885}} x=\frac{-15i}{\sqrt{-60e^{2}+885}}$$

Steps Using the Quadratic Formula

Combine 4x^{2} and -25x^{2} to get -21x^{2}.

$$15-4e^{2}x^{2}=25x^{2}+4\left(-21\right)x^{2}$$

Multiply 4 and -21 to get -84.

$$15-4e^{2}x^{2}=25x^{2}-84x^{2}$$

Combine 25x^{2} and -84x^{2} to get -59x^{2}.

$$15-4e^{2}x^{2}=-59x^{2}$$

Add 59x^{2} to both sides.

$$15-4e^{2}x^{2}+59x^{2}=0$$

Combine all terms containing x.

$$15+\left(-4e^{2}+59\right)x^{2}=0$$

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.

$$\left(-4e^{2}+59\right)x^{2}+15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4e^{2}+59 for a, 0 for b, and 15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4e^{2}+59\right)\times 15}}{2\left(-4e^{2}+59\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4e^{2}+59\right)\times 15}}{2\left(-4e^{2}+59\right)}$$

Multiply -4 times -4e^{2}+59.

$$x=\frac{0±\sqrt{\left(16e^{2}-236\right)\times 15}}{2\left(-4e^{2}+59\right)}$$

Multiply 16e^{2}-236 times 15.

$$x=\frac{0±\sqrt{240e^{2}-3540}}{2\left(-4e^{2}+59\right)}$$

Take the square root of 240e^{2}-3540.

$$x=\frac{0±2i\sqrt{-60e^{2}+885}}{2\left(-4e^{2}+59\right)}$$

Multiply 2 times -4e^{2}+59.

$$x=\frac{0±2i\sqrt{-60e^{2}+885}}{-8e^{2}+118}$$

Now solve the equation x=\frac{0±2i\sqrt{-60e^{2}+885}}{-8e^{2}+118} when ± is plus.

$$x=\frac{15i}{\sqrt{-60e^{2}+885}}$$

Now solve the equation x=\frac{0±2i\sqrt{-60e^{2}+885}}{-8e^{2}+118} when ± is minus.

$$x=\frac{-15i}{\sqrt{-60e^{2}+885}}$$

The equation is now solved.

$$x=\frac{15i}{\sqrt{-60e^{2}+885}} x=\frac{-15i}{\sqrt{-60e^{2}+885}}$$