What are the solutions to the equation completesquare 115+12.25t-4.9t^2 ?

The solutions to the equation completesquare 115+12.25t-4.9t^2 are -4.9(t-1.25)^2+122.65625

Find the zeros of completesquare 115+12.25t-4.9t^2

The zeros of completesquare 115+12.25t-4.9t^2 are -4.9(t-1.25)^2+122.65625

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complete the square

115 + 12.25 t - 4.9 t^{2}

- 4.9 (t - 1.25)^{2} + 122.65625

Solution steps

115 + 12.25 t - 4.9 t^{2}

Write in the standard form

a x^{2} + b x + c

- 4.9 t^{2} + 12.25 t + 115

Write

- 4.9 t^{2} + 12.25 t + 115

in the form:

x^{2} + 2 a x + a^{2}

Factor out

- 4.9

- 4.9 (t^{2} - \frac{12.25 t}{4.9} - \frac{115}{4.9})

2 a = - \frac{12.25}{4.9} : a = - 1.25

Add and subtract

(- 1.25)^{2}

- 4.9 (t^{2} - \frac{12.25 t}{4.9} - \frac{115}{4.9} + (- 1.25)^{2} - (- 1.25)^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

t^{2} - \frac{12.25}{4.9} t + (- 1.25)^{2} = (t - 1.25)^{2}

- 4.9 ((t - 1.25)^{2} - \frac{115}{4.9} - (- 1.25)^{2})

Simplify

- 4.9 (t - 1.25)^{2} + 122.65625

(m - 3) x^{2} + (m - 7) x + 2 = 0

2 x^{2} - 3 x = - 5

5 x^{2} + 7 = 27

0 = - x^{2} + 5 x - 4

2 n^{2} + 15 n + 7 = 0

What are the solutions to the equation completesquare 115+12.25t-4.9t^2 ?
The solutions to the equation completesquare 115+12.25t-4.9t^2 are -4.9(t-1.25)^2+122.65625
Find the zeros of completesquare 115+12.25t-4.9t^2
The zeros of completesquare 115+12.25t-4.9t^2 are -4.9(t-1.25)^2+122.65625