Solve 0.666^2+0.999^2=x^2

$${ 0.666 }^{ 2 } + { 0.999 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{333 \sqrt{13}}{1000} \approx 1.200648575$$

$$x = -\frac{333 \sqrt{13}}{1000} \approx -1.200648575$$

Steps by Finding Square Root

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=x^{2}$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=x^{2}$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=x^{2}$$

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

$$x^{2}=1.441557$$

Take the square root of both sides of the equation.

$$x=\frac{333\sqrt{13}}{1000} x=-\frac{333\sqrt{13}}{1000}$$

Steps Using the Quadratic Formula

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=x^{2}$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=x^{2}$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=x^{2}$$

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

$$x^{2}=1.441557$$

Subtract 1.441557 from both sides.

$$x^{2}-1.441557=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1.441557 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1.441557\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1.441557\right)}}{2}$$

Multiply -4 times -1.441557.

$$x=\frac{0±\sqrt{5.766228}}{2}$$

Take the square root of 5.766228.

$$x=\frac{0±\frac{333\sqrt{13}}{500}}{2}$$

Now solve the equation x=\frac{0±\frac{333\sqrt{13}}{500}}{2} when ± is plus.

$$x=\frac{333\sqrt{13}}{1000}$$

Now solve the equation x=\frac{0±\frac{333\sqrt{13}}{500}}{2} when ± is minus.

$$x=-\frac{333\sqrt{13}}{1000}$$

The equation is now solved.

$$x=\frac{333\sqrt{13}}{1000} x=-\frac{333\sqrt{13}}{1000}$$