Solve for w
w = \frac{4 \sqrt{70}}{7} \approx 4.780914437
w = -\frac{4 \sqrt{70}}{7} \approx -4.780914437
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\frac{160}{7}=w^{2}
Divide both sides by 7.
w^{2}=\frac{160}{7}
Swap sides so that all variable terms are on the left hand side.
w=\frac{4\sqrt{70}}{7} w=-\frac{4\sqrt{70}}{7}
Take the square root of both sides of the equation.
\frac{160}{7}=w^{2}
Divide both sides by 7.
w^{2}=\frac{160}{7}
Swap sides so that all variable terms are on the left hand side.
w^{2}-\frac{160}{7}=0
Subtract \frac{160}{7} from both sides.
w=\frac{0±\sqrt{0^{2}-4\left(-\frac{160}{7}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{160}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
w=\frac{0±\sqrt{-4\left(-\frac{160}{7}\right)}}{2}
Square 0.
w=\frac{0±\sqrt{\frac{640}{7}}}{2}
Multiply -4 times -\frac{160}{7}.
w=\frac{0±\frac{8\sqrt{70}}{7}}{2}
Take the square root of \frac{640}{7}.
w=\frac{4\sqrt{70}}{7}
Now solve the equation w=\frac{0±\frac{8\sqrt{70}}{7}}{2} when ± is plus.
w=-\frac{4\sqrt{70}}{7}
Now solve the equation w=\frac{0±\frac{8\sqrt{70}}{7}}{2} when ± is minus.
w=\frac{4\sqrt{70}}{7} w=-\frac{4\sqrt{70}}{7}
The equation is now solved.
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