Solve x=frac{12x+sqrt{-12x^2-4(5x^2)(50)}}{2}

$$x = \frac{ 12x+ \sqrt{ -12 { x }^{ 2 } -4(5 { x }^{ 2 } )(50) } }{ 2 }$$

Solve for x

$$x=0$$

Solution Steps

Multiply 4 and 5 to get 20.

$$x=\frac{12x+\sqrt{-12x^{2}-20x^{2}\times 50}}{2}$$

Multiply 20 and 50 to get 1000.

$$x=\frac{12x+\sqrt{-12x^{2}-1000x^{2}}}{2}$$

Combine -12x^{2} and -1000x^{2} to get -1012x^{2}.

$$x=\frac{12x+\sqrt{-1012x^{2}}}{2}$$

Subtract \frac{12x+\sqrt{-1012x^{2}}}{2} from both sides.

$$x-\frac{12x+\sqrt{-1012x^{2}}}{2}=0$$

Multiply both sides of the equation by 2.

$$2x-\left(12x+\sqrt{-1012x^{2}}\right)=0$$

To find the opposite of 12x+\sqrt{-1012x^{2}}, find the opposite of each term.

$$2x-12x-\sqrt{-1012x^{2}}=0$$

Combine 2x and -12x to get -10x.

$$-10x-\sqrt{-1012x^{2}}=0$$

Subtract -10x from both sides of the equation.

$$-\sqrt{-1012x^{2}}=10x$$

Square both sides of the equation.

$$\left(-\sqrt{-1012x^{2}}\right)^{2}=\left(10x\right)^{2}$$

Expand \left(-\sqrt{-1012x^{2}}\right)^{2}.

$$\left(-1\right)^{2}\left(\sqrt{-1012x^{2}}\right)^{2}=\left(10x\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1\left(\sqrt{-1012x^{2}}\right)^{2}=\left(10x\right)^{2}$$

Calculate \sqrt{-1012x^{2}} to the power of 2 and get -1012x^{2}.

$$1\left(-1012\right)x^{2}=\left(10x\right)^{2}$$

Multiply 1 and -1012 to get -1012.

$$-1012x^{2}=\left(10x\right)^{2}$$

Expand \left(10x\right)^{2}.

$$-1012x^{2}=10^{2}x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$-1012x^{2}=100x^{2}$$

Subtract 100x^{2} from both sides.

$$-1012x^{2}-100x^{2}=0$$

Combine -1012x^{2} and -100x^{2} to get -1112x^{2}.

$$-1112x^{2}=0$$

Divide both sides by -1112. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Substitute 0 for x in the equation x=\frac{12x+\sqrt{-12x^{2}-4\times 5x^{2}\times 50}}{2}.

$$0=\frac{12\times 0+\sqrt{-12\times 0^{2}-4\times 5\times 0^{2}\times 50}}{2}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation -\sqrt{-1012x^{2}}=10x has a unique solution.

$$x=0$$