Solve 5/68+29/6*x^2=2

$$\frac{ 5 }{ 6 } 8+2 \frac{ 9 }{ 6 } \times { x }^{ 2 } =2$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{3}i}{3}\approx -0-1.154700538i$$

$$x=\frac{2\sqrt{3}i}{3}\approx 1.154700538i$$

Steps by Finding Square Root

Multiply both sides of the equation by 6.

$$5\times 8+\left(2\times 6+9\right)x^{2}=12$$

Multiply 5 and 8 to get 40.

$$40+\left(2\times 6+9\right)x^{2}=12$$

Multiply 2 and 6 to get 12.

$$40+\left(12+9\right)x^{2}=12$$

Add 12 and 9 to get 21.

$$40+21x^{2}=12$$

Subtract 40 from both sides.

$$21x^{2}=12-40$$

Subtract 40 from 12 to get -28.

$$21x^{2}=-28$$

Divide both sides by 21.

$$x^{2}=\frac{-28}{21}$$

Reduce the fraction \frac{-28}{21} to lowest terms by extracting and canceling out 7.

$$x^{2}=-\frac{4}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{3}i}{3} x=-\frac{2\sqrt{3}i}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 6.

$$5\times 8+\left(2\times 6+9\right)x^{2}=12$$

Multiply 5 and 8 to get 40.

$$40+\left(2\times 6+9\right)x^{2}=12$$

Multiply 2 and 6 to get 12.

$$40+\left(12+9\right)x^{2}=12$$

Add 12 and 9 to get 21.

$$40+21x^{2}=12$$

Subtract 12 from both sides.

$$40+21x^{2}-12=0$$

Subtract 12 from 40 to get 28.

$$28+21x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$21x^{2}+28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 21 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 21\times 28}}{2\times 21}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 21\times 28}}{2\times 21}$$

Multiply -4 times 21.

$$x=\frac{0±\sqrt{-84\times 28}}{2\times 21}$$

Multiply -84 times 28.

$$x=\frac{0±\sqrt{-2352}}{2\times 21}$$

Take the square root of -2352.

$$x=\frac{0±28\sqrt{3}i}{2\times 21}$$

Multiply 2 times 21.

$$x=\frac{0±28\sqrt{3}i}{42}$$

Now solve the equation x=\frac{0±28\sqrt{3}i}{42} when ± is plus.

$$x=\frac{2\sqrt{3}i}{3}$$

Now solve the equation x=\frac{0±28\sqrt{3}i}{42} when ± is minus.

$$x=-\frac{2\sqrt{3}i}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{3}i}{3} x=-\frac{2\sqrt{3}i}{3}$$