Solve x^2+6x+4=3x^2+6x+5

$${ x }^{ 2 } +6x+4=3 { x }^{ 2 } +6x+5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Steps by Finding Square Root

Subtract 3x^{2} from both sides.

$$x^{2}+6x+4-3x^{2}=6x+5$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$-2x^{2}+6x+4=6x+5$$

Subtract 6x from both sides.

$$-2x^{2}+6x+4-6x=5$$

Combine 6x and -6x to get 0.

$$-2x^{2}+4=5$$

Subtract 4 from both sides.

$$-2x^{2}=5-4$$

Subtract 4 from 5 to get 1.

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

Divide both sides by -2.

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

The equation is now solved.

$$x=\frac{\sqrt{2}i}{2} x=-\frac{\sqrt{2}i}{2}$$

Steps Using the Quadratic Formula

Subtract 3x^{2} from both sides.

$$x^{2}+6x+4-3x^{2}=6x+5$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$-2x^{2}+6x+4=6x+5$$

Subtract 6x from both sides.

$$-2x^{2}+6x+4-6x=5$$

Combine 6x and -6x to get 0.

$$-2x^{2}+4=5$$

Subtract 5 from both sides.

$$-2x^{2}+4-5=0$$

Subtract 5 from 4 to get -1.

$$-2x^{2}-1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-1\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-1\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-1\right)}}{2\left(-2\right)}$$

Multiply 8 times -1.

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

Take the square root of -8.

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

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{2}i}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{-4} when ± is plus.

$$x=-\frac{\sqrt{2}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}i}{-4} when ± is minus.

$$x=\frac{\sqrt{2}i}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{2}i}{2} x=\frac{\sqrt{2}i}{2}$$