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