Solve 64(5+x^2)=(18-3x^2)

$$64(5+ { x }^{ 2 } )=(18-3 { x }^{ 2 } )$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{20234}i}{67}\approx -0-2.123078587i$$

$$x=\frac{\sqrt{20234}i}{67}\approx 2.123078587i$$

Steps by Finding Square Root

Use the distributive property to multiply 64 by 5+x^{2}.

$$320+64x^{2}=18-3x^{2}$$

Add 3x^{2} to both sides.

$$320+64x^{2}+3x^{2}=18$$

Combine 64x^{2} and 3x^{2} to get 67x^{2}.

$$320+67x^{2}=18$$

Subtract 320 from both sides.

$$67x^{2}=18-320$$

Subtract 320 from 18 to get -302.

$$67x^{2}=-302$$

Divide both sides by 67.

$$x^{2}=-\frac{302}{67}$$

The equation is now solved.

$$x=\frac{\sqrt{20234}i}{67} x=-\frac{\sqrt{20234}i}{67}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 64 by 5+x^{2}.

$$320+64x^{2}=18-3x^{2}$$

Subtract 18 from both sides.

$$320+64x^{2}-18=-3x^{2}$$

Subtract 18 from 320 to get 302.

$$302+64x^{2}=-3x^{2}$$

Add 3x^{2} to both sides.

$$302+64x^{2}+3x^{2}=0$$

Combine 64x^{2} and 3x^{2} to get 67x^{2}.

$$302+67x^{2}=0$$

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.

$$67x^{2}+302=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 67 for a, 0 for b, and 302 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 67\times 302}}{2\times 67}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 67\times 302}}{2\times 67}$$

Multiply -4 times 67.

$$x=\frac{0±\sqrt{-268\times 302}}{2\times 67}$$

Multiply -268 times 302.

$$x=\frac{0±\sqrt{-80936}}{2\times 67}$$

Take the square root of -80936.

$$x=\frac{0±2\sqrt{20234}i}{2\times 67}$$

Multiply 2 times 67.

$$x=\frac{0±2\sqrt{20234}i}{134}$$

Now solve the equation x=\frac{0±2\sqrt{20234}i}{134} when ± is plus.

$$x=\frac{\sqrt{20234}i}{67}$$

Now solve the equation x=\frac{0±2\sqrt{20234}i}{134} when ± is minus.

$$x=-\frac{\sqrt{20234}i}{67}$$

The equation is now solved.

$$x=\frac{\sqrt{20234}i}{67} x=-\frac{\sqrt{20234}i}{67}$$