Solve for w
w=-\sqrt{7}\approx -2.645751311
w=\sqrt{7}\approx 2.645751311
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t^{2}-3t-28=0
Substitute t for w^{2}.
t=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\left(-28\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -3 for b, and -28 for c in the quadratic formula.
t=\frac{3±11}{2}
Do the calculations.
t=7 t=-4
Solve the equation t=\frac{3±11}{2} when ± is plus and when ± is minus.
w=\sqrt{7} w=-\sqrt{7}
Since w=t^{2}, the solutions are obtained by evaluating w=±\sqrt{t} for positive t.
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