Solve 6^2-x^2=2*25*4

$$6 ^ { 2 } - x ^ { 2 } = 2 \times 25 \times 4$$

Solve for x (complex solution)

$$x=-2\sqrt{41}i\approx -0-12.806248475i$$

$$x=2\sqrt{41}i\approx 12.806248475i$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36-x^{2}=2\times 25\times 4$$

Multiply 2 and 25 to get 50.

$$36-x^{2}=50\times 4$$

Multiply 50 and 4 to get 200.

$$36-x^{2}=200$$

Subtract 36 from both sides.

$$-x^{2}=200-36$$

Subtract 36 from 200 to get 164.

$$-x^{2}=164$$

Divide both sides by -1.

$$x^{2}=-164$$

The equation is now solved.

$$x=2\sqrt{41}i x=-2\sqrt{41}i$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36-x^{2}=2\times 25\times 4$$

Multiply 2 and 25 to get 50.

$$36-x^{2}=50\times 4$$

Multiply 50 and 4 to get 200.

$$36-x^{2}=200$$

Subtract 200 from both sides.

$$36-x^{2}-200=0$$

Subtract 200 from 36 to get -164.

$$-164-x^{2}=0$$

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.

$$-x^{2}-164=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -164 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-164\right)}}{2\left(-1\right)}$$

Multiply 4 times -164.

$$x=\frac{0±\sqrt{-656}}{2\left(-1\right)}$$

Take the square root of -656.

$$x=\frac{0±4\sqrt{41}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4\sqrt{41}i}{-2}$$

Now solve the equation x=\frac{0±4\sqrt{41}i}{-2} when ± is plus.

$$x=-2\sqrt{41}i$$

Now solve the equation x=\frac{0±4\sqrt{41}i}{-2} when ± is minus.

$$x=2\sqrt{41}i$$

The equation is now solved.

$$x=-2\sqrt{41}i x=2\sqrt{41}i$$