Solve 3^4+b^2=6^4

$$3 ^ { 4 } + b ^ { 2 } = 6 ^ { 4 }$$

Solve for b

$$b=9\sqrt{15}\approx 34.856850116$$

$$b=-9\sqrt{15}\approx -34.856850116$$

Steps by Finding Square Root

Calculate 3 to the power of 4 and get 81.

$$81+b^{2}=6^{4}$$

Calculate 6 to the power of 4 and get 1296.

$$81+b^{2}=1296$$

Subtract 81 from both sides.

$$b^{2}=1296-81$$

Subtract 81 from 1296 to get 1215.

$$b^{2}=1215$$

Take the square root of both sides of the equation.

$$b=9\sqrt{15} b=-9\sqrt{15}$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 4 and get 81.

$$81+b^{2}=6^{4}$$

Calculate 6 to the power of 4 and get 1296.

$$81+b^{2}=1296$$

Subtract 1296 from both sides.

$$81+b^{2}-1296=0$$

Subtract 1296 from 81 to get -1215.

$$-1215+b^{2}=0$$

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.

$$b^{2}-1215=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1215 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-1215\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-1215\right)}}{2}$$

Multiply -4 times -1215.

$$b=\frac{0±\sqrt{4860}}{2}$$

Take the square root of 4860.

$$b=\frac{0±18\sqrt{15}}{2}$$

Now solve the equation b=\frac{0±18\sqrt{15}}{2} when ± is plus.

$$b=9\sqrt{15}$$

Now solve the equation b=\frac{0±18\sqrt{15}}{2} when ± is minus.

$$b=-9\sqrt{15}$$

The equation is now solved.

$$b=9\sqrt{15} b=-9\sqrt{15}$$