What are the solutions to the equation (t)=-t^2+22t-85 ?

The solutions to the equation (t)=-t^2+22t-85 are t=(21-sqrt(101))/2 ,t=(21+sqrt(101))/2

Find the zeros of (t)=-t^2+22t-85

The zeros of (t)=-t^2+22t-85 are t=(21-sqrt(101))/2 ,t=(21+sqrt(101))/2

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(t) = - t^{2} + 22 t - 85

t = \frac{21 - 101}{2}, t = \frac{21 + 101}{2}

Decimal Notation

t = 5.47506 \dots, t = 15.52493 \dots

Solution steps

(t) = - t^{2} + 22 t - 85

Refine

t = - t^{2} + 22 t - 85

Switch sides

- t^{2} + 22 t - 85 = t

Move

t

to the left side

- t^{2} + 21 t - 85 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 21 \pm 2 1 ^{2} - 4 ( - 1 ) ( - 85 )}{2 ( - 1 )}

2 1^{2} - 4 (- 1) (- 85) = 101

t_{1, 2} = \frac{- 21 \pm 101}{2 ( - 1 )}

Separate the solutions

t_{1} = \frac{- 21 + 101}{2 ( - 1 )}, t_{2} = \frac{- 21 - 101}{2 ( - 1 )}

t = \frac{- 21 + 101}{2 ( - 1 )} : \frac{21 - 101}{2}

t = \frac{- 21 - 101}{2 ( - 1 )} : \frac{21 + 101}{2}

The solutions to the quadratic equation are:

t = \frac{21 - 101}{2}, t = \frac{21 + 101}{2}

x, a = (x - 5)^{2} + 5 y^{6} - 30

\frac{2 x ^{2}}{3} = 32

3 x^{2} + 25 x - 5 = 0

2 - 5 k = \frac{k ^{2}}{3}

t, a^{2} b^{2} t^{2} - a^{2} t = 1 - b^{2} t

What are the solutions to the equation (t)=-t^2+22t-85 ?
The solutions to the equation (t)=-t^2+22t-85 are t=(21-sqrt(101))/2 ,t=(21+sqrt(101))/2
Find the zeros of (t)=-t^2+22t-85
The zeros of (t)=-t^2+22t-85 are t=(21-sqrt(101))/2 ,t=(21+sqrt(101))/2