Solve 0.666^2+0.999^2=1x^2+1.5

$${ 0.666 }^{ 2 } + { 0.999 }^{ 2 } = 1 { x }^{ 2 } +1.5$$

Solve for x (complex solution)

$$x=-\frac{i\times 11\sqrt{483}}{1000}\approx -0-0.241749871i$$

$$x=\frac{i\times 11\sqrt{483}}{1000}\approx 0.241749871i$$

Steps by Finding Square Root

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=1x^{2}+1.5$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=1x^{2}+1.5$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=1x^{2}+1.5$$

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

$$1x^{2}+1.5=1.441557$$

Subtract 1.5 from both sides.

$$1x^{2}=1.441557-1.5$$

Subtract 1.5 from 1.441557 to get -0.058443.

$$1x^{2}=-0.058443$$

Divide both sides by 1.

$$x^{2}=\frac{-0.058443}{1}$$

Expand \frac{-0.058443}{1} by multiplying both numerator and the denominator by 1000000.

$$x^{2}=\frac{-58443}{1000000}$$

Fraction \frac{-58443}{1000000} can be rewritten as -\frac{58443}{1000000} by extracting the negative sign.

$$x^{2}=-\frac{58443}{1000000}$$

The equation is now solved.

$$x=\frac{11\sqrt{483}i}{1000} x=-\frac{11\sqrt{483}i}{1000}$$

Steps Using the Quadratic Formula

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=1x^{2}+1.5$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=1x^{2}+1.5$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=1x^{2}+1.5$$

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

$$1x^{2}+1.5=1.441557$$

Subtract 1.441557 from both sides.

$$1x^{2}+1.5-1.441557=0$$

Subtract 1.441557 from 1.5 to get 0.058443.

$$1x^{2}+0.058443=0$$

Reorder the terms.

$$x^{2}+0.058443=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0.058443 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.058443}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.058443}}{2}$$

Multiply -4 times 0.058443.

$$x=\frac{0±\sqrt{-0.233772}}{2}$$

Take the square root of -0.233772.

$$x=\frac{0±\frac{11\sqrt{483}i}{500}}{2}$$

Now solve the equation x=\frac{0±\frac{11\sqrt{483}i}{500}}{2} when ± is plus.

$$x=\frac{11\sqrt{483}i}{1000}$$

Now solve the equation x=\frac{0±\frac{11\sqrt{483}i}{500}}{2} when ± is minus.

$$x=-\frac{11\sqrt{483}i}{1000}$$

The equation is now solved.

$$x=\frac{11\sqrt{483}i}{1000} x=-\frac{11\sqrt{483}i}{1000}$$