What are the solutions to the equation 9t^2=36t-1 ?

The solutions to the equation 9t^2=36t-1 are t=(6+sqrt(35))/3 ,t=(6-sqrt(35))/3

Find the zeros of 9t^2=36t-1

The zeros of 9t^2=36t-1 are t=(6+sqrt(35))/3 ,t=(6-sqrt(35))/3

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9 t^{2} = 36 t - 1

t = \frac{6 + 35}{3}, t = \frac{6 - 35}{3}

Solution steps

9 t^{2} = 36 t - 1

Move

1

to the left side

9 t^{2} + 1 = 36 t

Move

36 t

to the left side

9 t^{2} + 1 - 36 t = 0

Write in the standard form

a x^{2} + b x + c = 0

9 t^{2} - 36 t + 1 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 36 ) \pm ( - 36 ) ^{2} - 4 \cdot 9 \cdot 1}{2 \cdot 9}

(- 36)^{2} - 4 \cdot 9 \cdot 1 = 635

t_{1, 2} = \frac{- ( - 36 ) \pm 6 35}{2 \cdot 9}

Separate the solutions

t_{1} = \frac{- ( - 36 ) + 6 35}{2 \cdot 9}, t_{2} = \frac{- ( - 36 ) - 6 35}{2 \cdot 9}

t = \frac{- ( - 36 ) + 6 35}{2 \cdot 9} : \frac{6 + 35}{3}

t = \frac{- ( - 36 ) - 6 35}{2 \cdot 9} : \frac{6 - 35}{3}

The solutions to the quadratic equation are:

t = \frac{6 + 35}{3}, t = \frac{6 - 35}{3}

\frac{1}{4} x^{2} + \frac{2}{3} x = 0

2 x^{2} - 7 x - 10 = 0

3 x^{2} + 11 x + 7 = 0

5 x^{2} - 90 x = - 370

(x + 1)^{2} = - 9

What are the solutions to the equation 9t^2=36t-1 ?
The solutions to the equation 9t^2=36t-1 are t=(6+sqrt(35))/3 ,t=(6-sqrt(35))/3
Find the zeros of 9t^2=36t-1
The zeros of 9t^2=36t-1 are t=(6+sqrt(35))/3 ,t=(6-sqrt(35))/3