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y^{2}=64
Calculate 4 to the power of 3 and get 64.
y^{2}-64=0
Subtract 64 from both sides.
\left(y-8\right)\left(y+8\right)=0
Consider y^{2}-64. Rewrite y^{2}-64 as y^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
y=8 y=-8
To find equation solutions, solve y-8=0 and y+8=0.
y^{2}=64
Calculate 4 to the power of 3 and get 64.
y=8 y=-8
Take the square root of both sides of the equation.
y^{2}=64
Calculate 4 to the power of 3 and get 64.
y^{2}-64=0
Subtract 64 from both sides.
y=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
y=\frac{0±\sqrt{-4\left(-64\right)}}{2}
Square 0.
y=\frac{0±\sqrt{256}}{2}
Multiply -4 times -64.
y=\frac{0±16}{2}
Take the square root of 256.
y=8
Now solve the equation y=\frac{0±16}{2} when ± is plus. Divide 16 by 2.
y=-8
Now solve the equation y=\frac{0±16}{2} when ± is minus. Divide -16 by 2.
y=8 y=-8
The equation is now solved.