Solve 0.666^2+0.999^2=1x^2+2.3

$${ 0.666 }^{ 2 } + { 0.999 }^{ 2 } = 1 { x }^{ 2 } +2.3$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{858443}}{1000}\approx -0-0.926521991i$$

$$x=\frac{i\sqrt{858443}}{1000}\approx 0.926521991i$$

Steps by Finding Square Root

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=1x^{2}+2.3$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=1x^{2}+2.3$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=1x^{2}+2.3$$

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

$$1x^{2}+2.3=1.441557$$

Subtract 2.3 from both sides.

$$1x^{2}=1.441557-2.3$$

Subtract 2.3 from 1.441557 to get -0.858443.

$$1x^{2}=-0.858443$$

Divide both sides by 1.

$$x^{2}=\frac{-0.858443}{1}$$

Expand \frac{-0.858443}{1} by multiplying both numerator and the denominator by 1000000.

$$x^{2}=\frac{-858443}{1000000}$$

Fraction \frac{-858443}{1000000} can be rewritten as -\frac{858443}{1000000} by extracting the negative sign.

$$x^{2}=-\frac{858443}{1000000}$$

The equation is now solved.

$$x=\frac{\sqrt{858443}i}{1000} x=-\frac{\sqrt{858443}i}{1000}$$

Steps Using the Quadratic Formula

Calculate 0.666 to the power of 2 and get 0.443556.

$$0.443556+0.999^{2}=1x^{2}+2.3$$

Calculate 0.999 to the power of 2 and get 0.998001.

$$0.443556+0.998001=1x^{2}+2.3$$

Add 0.443556 and 0.998001 to get 1.441557.

$$1.441557=1x^{2}+2.3$$

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

$$1x^{2}+2.3=1.441557$$

Subtract 1.441557 from both sides.

$$1x^{2}+2.3-1.441557=0$$

Subtract 1.441557 from 2.3 to get 0.858443.

$$1x^{2}+0.858443=0$$

Reorder the terms.

$$x^{2}+0.858443=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0.858443 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.858443}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.858443}}{2}$$

Multiply -4 times 0.858443.

$$x=\frac{0±\sqrt{-3.433772}}{2}$$

Take the square root of -3.433772.

$$x=\frac{0±\frac{\sqrt{858443}i}{500}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{858443}i}{500}}{2} when ± is plus.

$$x=\frac{\sqrt{858443}i}{1000}$$

Now solve the equation x=\frac{0±\frac{\sqrt{858443}i}{500}}{2} when ± is minus.

$$x=-\frac{\sqrt{858443}i}{1000}$$

The equation is now solved.

$$x=\frac{\sqrt{858443}i}{1000} x=-\frac{\sqrt{858443}i}{1000}$$