Solve 46^4+3b^2-36=0

$$46 ^ { 4 } + 3 b ^ { 2 } - 36 = 0$$

Solve for b

$$b=-\frac{2\sqrt{3358065}i}{3}\approx -0-1221.668258298i$$

$$b=\frac{2\sqrt{3358065}i}{3}\approx 1221.668258298i$$

Steps by Finding Square Root

Calculate 46 to the power of 4 and get 4477456.

$$4477456+3b^{2}-36=0$$

Subtract 36 from 4477456 to get 4477420.

$$4477420+3b^{2}=0$$

Subtract 4477420 from both sides. Anything subtracted from zero gives its negation.

$$3b^{2}=-4477420$$

Divide both sides by 3.

$$b^{2}=-\frac{4477420}{3}$$

The equation is now solved.

$$b=\frac{2\sqrt{3358065}i}{3} b=-\frac{2\sqrt{3358065}i}{3}$$

Steps Using the Quadratic Formula

Calculate 46 to the power of 4 and get 4477456.

$$4477456+3b^{2}-36=0$$

Subtract 36 from 4477456 to get 4477420.

$$4477420+3b^{2}=0$$

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.

$$3b^{2}+4477420=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and 4477420 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 3\times 4477420}}{2\times 3}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 3\times 4477420}}{2\times 3}$$

Multiply -4 times 3.

$$b=\frac{0±\sqrt{-12\times 4477420}}{2\times 3}$$

Multiply -12 times 4477420.

$$b=\frac{0±\sqrt{-53729040}}{2\times 3}$$

Take the square root of -53729040.

$$b=\frac{0±4\sqrt{3358065}i}{2\times 3}$$

Multiply 2 times 3.

$$b=\frac{0±4\sqrt{3358065}i}{6}$$

Now solve the equation b=\frac{0±4\sqrt{3358065}i}{6} when ± is plus.

$$b=\frac{2\sqrt{3358065}i}{3}$$

Now solve the equation b=\frac{0±4\sqrt{3358065}i}{6} when ± is minus.

$$b=-\frac{2\sqrt{3358065}i}{3}$$

The equation is now solved.

$$b=\frac{2\sqrt{3358065}i}{3} b=-\frac{2\sqrt{3358065}i}{3}$$