Solve for z
z=-2\sqrt{2}\approx -2.828427125
z=2\sqrt{2}\approx 2.828427125
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-t^{2}+7t+8=0
Substitute t for z^{2}.
t=\frac{-7±\sqrt{7^{2}-4\left(-1\right)\times 8}}{-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, 7 for b, and 8 for c in the quadratic formula.
t=\frac{-7±9}{-2}
Do the calculations.
t=-1 t=8
Solve the equation t=\frac{-7±9}{-2} when ± is plus and when ± is minus.
z=2\sqrt{2} z=-2\sqrt{2}
Since z=t^{2}, the solutions are obtained by evaluating z=±\sqrt{t} for positive t.
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