What are the solutions to the equation 75^2=(15t)^2+[12(t-2)]^2 ?

The solutions to the equation 75^2=(15t)^2+[12(t-2)]^2 are t= 187/41 ,t=-3

Find the zeros of 75^2=(15t)^2+[12(t-2)]^2

The zeros of 75^2=(15t)^2+[12(t-2)]^2 are t= 187/41 ,t=-3

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7 5^{2} = (15 t)^{2} + [12 (t - 2)]^{2}

t = \frac{187}{41}, t = - 3

Decimal Notation

t = 4.56097 \dots, t = - 3

Solution steps

7 5^{2} = (15 t)^{2} + [12 (t - 2)]^{2}

Expand

7 5^{2} : 5625

Expand

(15 t)^{2} + (12 (t - 2))^{2} : 369 t^{2} - 576 t + 576

5625 = 369 t^{2} - 576 t + 576

Switch sides

369 t^{2} - 576 t + 576 = 5625

Move

5625

to the left side

369 t^{2} - 576 t - 5049 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 576 ) \pm ( - 576 ) ^{2} - 4 \cdot 369 ( - 5049 )}{2 \cdot 369}

(- 576)^{2} - 4 \cdot 369 (- 5049) = 2790

t_{1, 2} = \frac{- ( - 576 ) \pm 2790}{2 \cdot 369}

Separate the solutions

t_{1} = \frac{- ( - 576 ) + 2790}{2 \cdot 369}, t_{2} = \frac{- ( - 576 ) - 2790}{2 \cdot 369}

t = \frac{- ( - 576 ) + 2790}{2 \cdot 369} : \frac{187}{41}

t = \frac{- ( - 576 ) - 2790}{2 \cdot 369} : - 3

The solutions to the quadratic equation are:

t = \frac{187}{41}, t = - 3

\frac{3 x ^{2} - x}{3} = 0

\frac{1}{3} \frac{x ^{2}}{3} = - 18

33 x^{2} - 5 x - 9 = 0

\frac{5}{2} = \frac{5 x ^{2}}{4}

x, z = x^{2} + y^{2} - 4

What are the solutions to the equation 75^2=(15t)^2+[12(t-2)]^2 ?
The solutions to the equation 75^2=(15t)^2+[12(t-2)]^2 are t= 187/41 ,t=-3
Find the zeros of 75^2=(15t)^2+[12(t-2)]^2
The zeros of 75^2=(15t)^2+[12(t-2)]^2 are t= 187/41 ,t=-3