Solve D^2+8^2=|7^2

$$D ^ { 2 } + 8 ^ { 2 } = | 7 ^ { 2 }$$

Solve for D

$$D=-\sqrt{15}i\approx -0-3.872983346i$$

$$D=\sqrt{15}i\approx 3.872983346i$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$D^{2}+64=|7^{2}|$$

Calculate 7 to the power of 2 and get 49.

$$D^{2}+64=|49|$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 49 is 49.

$$D^{2}+64=49$$

Subtract 64 from both sides.

$$D^{2}=49-64$$

Subtract 64 from 49 to get -15.

$$D^{2}=-15$$

The equation is now solved.

$$D=\sqrt{15}i D=-\sqrt{15}i$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$D^{2}+64=|7^{2}|$$

Calculate 7 to the power of 2 and get 49.

$$D^{2}+64=|49|$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 49 is 49.

$$D^{2}+64=49$$

Subtract 49 from both sides.

$$D^{2}+64-49=0$$

Subtract 49 from 64 to get 15.

$$D^{2}+15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\times 15}}{2}$$

Square 0.

$$D=\frac{0±\sqrt{-4\times 15}}{2}$$

Multiply -4 times 15.

$$D=\frac{0±\sqrt{-60}}{2}$$

Take the square root of -60.

$$D=\frac{0±2\sqrt{15}i}{2}$$

Now solve the equation D=\frac{0±2\sqrt{15}i}{2} when ± is plus.

$$D=\sqrt{15}i$$

Now solve the equation D=\frac{0±2\sqrt{15}i}{2} when ± is minus.

$$D=-\sqrt{15}i$$

The equation is now solved.

$$D=\sqrt{15}i D=-\sqrt{15}i$$