Solve (9x)^2-(12x)^2=6300

$$( 9 x ) ^ { 2 } - ( 12 x ) ^ { 2 } = 6300$$

Solve for x (complex solution)

$$x=10i$$

$$x=-10i$$

Steps by Finding Square Root

Expand \left(9x\right)^{2}.

$$9^{2}x^{2}-\left(12x\right)^{2}=6300$$

Calculate 9 to the power of 2 and get 81.

$$81x^{2}-\left(12x\right)^{2}=6300$$

Expand \left(12x\right)^{2}.

$$81x^{2}-12^{2}x^{2}=6300$$

Calculate 12 to the power of 2 and get 144.

$$81x^{2}-144x^{2}=6300$$

Combine 81x^{2} and -144x^{2} to get -63x^{2}.

$$-63x^{2}=6300$$

Divide both sides by -63.

$$x^{2}=\frac{6300}{-63}$$

Divide 6300 by -63 to get -100.

$$x^{2}=-100$$

The equation is now solved.

$$x=10i x=-10i$$

Steps Using the Quadratic Formula

Expand \left(9x\right)^{2}.

$$9^{2}x^{2}-\left(12x\right)^{2}=6300$$

Calculate 9 to the power of 2 and get 81.

$$81x^{2}-\left(12x\right)^{2}=6300$$

Expand \left(12x\right)^{2}.

$$81x^{2}-12^{2}x^{2}=6300$$

Calculate 12 to the power of 2 and get 144.

$$81x^{2}-144x^{2}=6300$$

Combine 81x^{2} and -144x^{2} to get -63x^{2}.

$$-63x^{2}=6300$$

Subtract 6300 from both sides.

$$-63x^{2}-6300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -63 for a, 0 for b, and -6300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-63\right)\left(-6300\right)}}{2\left(-63\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-63\right)\left(-6300\right)}}{2\left(-63\right)}$$

Multiply -4 times -63.

$$x=\frac{0±\sqrt{252\left(-6300\right)}}{2\left(-63\right)}$$

Multiply 252 times -6300.

$$x=\frac{0±\sqrt{-1587600}}{2\left(-63\right)}$$

Take the square root of -1587600.

$$x=\frac{0±1260i}{2\left(-63\right)}$$

Multiply 2 times -63.

$$x=\frac{0±1260i}{-126}$$

Now solve the equation x=\frac{0±1260i}{-126} when ± is plus.

$$x=-10i$$

Now solve the equation x=\frac{0±1260i}{-126} when ± is minus.

$$x=10i$$

The equation is now solved.

$$x=-10i x=10i$$