Solve 10^2/1=D^2/1+D^2/1

$$\frac { 10 ^ { 2 } } { 1 } = \frac { D ^ { 2 } } { 1 } + \frac { D ^ { 2 } } { 1 }$$

Solve for D

$$D=5\sqrt{2}\approx 7.071067812$$

$$D=-5\sqrt{2}\approx -7.071067812$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$\frac{100}{1}=\frac{D^{2}}{1}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=\frac{D^{2}}{1}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=D^{2}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=D^{2}+D^{2}$$

Combine D^{2} and D^{2} to get 2D^{2}.

$$100=2D^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2D^{2}=100$$

Divide both sides by 2.

$$D^{2}=\frac{100}{2}$$

Divide 100 by 2 to get 50.

$$D^{2}=50$$

Take the square root of both sides of the equation.

$$D=5\sqrt{2} D=-5\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$\frac{100}{1}=\frac{D^{2}}{1}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=\frac{D^{2}}{1}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=D^{2}+\frac{D^{2}}{1}$$

Anything divided by one gives itself.

$$100=D^{2}+D^{2}$$

Combine D^{2} and D^{2} to get 2D^{2}.

$$100=2D^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2D^{2}=100$$

Subtract 100 from both sides.

$$2D^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\times 2\left(-100\right)}}{2\times 2}$$

Square 0.

$$D=\frac{0±\sqrt{-4\times 2\left(-100\right)}}{2\times 2}$$

Multiply -4 times 2.

$$D=\frac{0±\sqrt{-8\left(-100\right)}}{2\times 2}$$

Multiply -8 times -100.

$$D=\frac{0±\sqrt{800}}{2\times 2}$$

Take the square root of 800.

$$D=\frac{0±20\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$D=\frac{0±20\sqrt{2}}{4}$$

Now solve the equation D=\frac{0±20\sqrt{2}}{4} when ± is plus.

$$D=5\sqrt{2}$$

Now solve the equation D=\frac{0±20\sqrt{2}}{4} when ± is minus.

$$D=-5\sqrt{2}$$

The equation is now solved.

$$D=5\sqrt{2} D=-5\sqrt{2}$$