Solve 16^2-2*14^2-x^2=2*16*14

$$16 ^ { 2 } - 2 \cdot 14 ^ { 2 } - x ^ { 2 } = 2 \cdot 16 \cdot 14$$

Solve for x (complex solution)

$$x=-2\sqrt{146}i\approx -0-24.166091947i$$

$$x=2\sqrt{146}i\approx 24.166091947i$$

Steps by Finding Square Root

Calculate 16 to the power of 2 and get 256.

$$256-2\times 14^{2}-x^{2}=2\times 16\times 14$$

Calculate 14 to the power of 2 and get 196.

$$256-2\times 196-x^{2}=2\times 16\times 14$$

Multiply 2 and 196 to get 392.

$$256-392-x^{2}=2\times 16\times 14$$

Subtract 392 from 256 to get -136.

$$-136-x^{2}=2\times 16\times 14$$

Multiply 2 and 16 to get 32.

$$-136-x^{2}=32\times 14$$

Multiply 32 and 14 to get 448.

$$-136-x^{2}=448$$

Add 136 to both sides.

$$-x^{2}=448+136$$

Add 448 and 136 to get 584.

$$-x^{2}=584$$

Divide both sides by -1.

$$x^{2}=-584$$

The equation is now solved.

$$x=2\sqrt{146}i x=-2\sqrt{146}i$$

Steps Using the Quadratic Formula

Calculate 16 to the power of 2 and get 256.

$$256-2\times 14^{2}-x^{2}=2\times 16\times 14$$

Calculate 14 to the power of 2 and get 196.

$$256-2\times 196-x^{2}=2\times 16\times 14$$

Multiply 2 and 196 to get 392.

$$256-392-x^{2}=2\times 16\times 14$$

Subtract 392 from 256 to get -136.

$$-136-x^{2}=2\times 16\times 14$$

Multiply 2 and 16 to get 32.

$$-136-x^{2}=32\times 14$$

Multiply 32 and 14 to get 448.

$$-136-x^{2}=448$$

Subtract 448 from both sides.

$$-136-x^{2}-448=0$$

Subtract 448 from -136 to get -584.

$$-584-x^{2}=0$$

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.

$$-x^{2}-584=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -584 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-584\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-584\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-584\right)}}{2\left(-1\right)}$$

Multiply 4 times -584.

$$x=\frac{0±\sqrt{-2336}}{2\left(-1\right)}$$

Take the square root of -2336.

$$x=\frac{0±4\sqrt{146}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4\sqrt{146}i}{-2}$$

Now solve the equation x=\frac{0±4\sqrt{146}i}{-2} when ± is plus.

$$x=-2\sqrt{146}i$$

Now solve the equation x=\frac{0±4\sqrt{146}i}{-2} when ± is minus.

$$x=2\sqrt{146}i$$

The equation is now solved.

$$x=-2\sqrt{146}i x=2\sqrt{146}i$$