Solve left(1*8right)^2+d^2=left(3-0*6right)^2

$${ \left(1 \cdot 8 \right) }^{ 2 } + { d }^{ 2 } = { \left(3-0 \cdot 6 \right) }^{ 2 }$$

Solve for d

$$d=-\sqrt{55}i\approx -0-7.416198487i$$

$$d=\sqrt{55}i\approx 7.416198487i$$

Steps by Finding Square Root

Multiply 1 and 8 to get 8.

$$8^{2}+d^{2}=\left(3-0\times 6\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64+d^{2}=\left(3-0\times 6\right)^{2}$$

Multiply 0 and 6 to get 0.

$$64+d^{2}=\left(3-0\right)^{2}$$

Subtract 0 from 3 to get 3.

$$64+d^{2}=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$64+d^{2}=9$$

Subtract 64 from both sides.

$$d^{2}=9-64$$

Subtract 64 from 9 to get -55.

$$d^{2}=-55$$

The equation is now solved.

$$d=\sqrt{55}i d=-\sqrt{55}i$$

Steps Using the Quadratic Formula

Multiply 1 and 8 to get 8.

$$8^{2}+d^{2}=\left(3-0\times 6\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$64+d^{2}=\left(3-0\times 6\right)^{2}$$

Multiply 0 and 6 to get 0.

$$64+d^{2}=\left(3-0\right)^{2}$$

Subtract 0 from 3 to get 3.

$$64+d^{2}=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$64+d^{2}=9$$

Subtract 9 from both sides.

$$64+d^{2}-9=0$$

Subtract 9 from 64 to get 55.

$$55+d^{2}=0$$

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.

$$d^{2}+55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$d=\frac{0±\sqrt{0^{2}-4\times 55}}{2}$$

Square 0.

$$d=\frac{0±\sqrt{-4\times 55}}{2}$$

Multiply -4 times 55.

$$d=\frac{0±\sqrt{-220}}{2}$$

Take the square root of -220.

$$d=\frac{0±2\sqrt{55}i}{2}$$

Now solve the equation d=\frac{0±2\sqrt{55}i}{2} when ± is plus.

$$d=\sqrt{55}i$$

Now solve the equation d=\frac{0±2\sqrt{55}i}{2} when ± is minus.

$$d=-\sqrt{55}i$$

The equation is now solved.

$$d=\sqrt{55}i d=-\sqrt{55}i$$