What are the solutions to the equation 4(x-3)^2-25(x-2)^2=0 ?

The solutions to the equation 4(x-3)^2-25(x-2)^2=0 are x= 4/3 ,x= 16/7

Find the zeros of 4(x-3)^2-25(x-2)^2=0

The zeros of 4(x-3)^2-25(x-2)^2=0 are x= 4/3 ,x= 16/7

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4 (x - 3)^{2} - 25 (x - 2)^{2} = 0

x = \frac{4}{3}, x = \frac{16}{7}

Decimal Notation

x = 1.33333 \dots, x = 2.28571 \dots

Solution steps

4 (x - 3)^{2} - 25 (x - 2)^{2} = 0

Expand

4 (x - 3)^{2} - 25 (x - 2)^{2} : - 21 x^{2} + 76 x - 64

- 21 x^{2} + 76 x - 64 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 76 \pm 7 6 ^{2} - 4 ( - 21 ) ( - 64 )}{2 ( - 21 )}

7 6^{2} - 4 (- 21) (- 64) = 20

x_{1, 2} = \frac{- 76 \pm 20}{2 ( - 21 )}

Separate the solutions

x_{1} = \frac{- 76 + 20}{2 ( - 21 )}, x_{2} = \frac{- 76 - 20}{2 ( - 21 )}

x = \frac{- 76 + 20}{2 ( - 21 )} : \frac{4}{3}

x = \frac{- 76 - 20}{2 ( - 21 )} : \frac{16}{7}

The solutions to the quadratic equation are:

x = \frac{4}{3}, x = \frac{16}{7}

3 m^{2} + 9 m = 0

- 3 m + 2 m^{2} + 7 = 0

9 x^{2} + 4 (0)^{2} = 36

(x - 1) (2 x - 2) = 3

8 t (t + 3) = 2 t - 5

What are the solutions to the equation 4(x-3)^2-25(x-2)^2=0 ?
The solutions to the equation 4(x-3)^2-25(x-2)^2=0 are x= 4/3 ,x= 16/7
Find the zeros of 4(x-3)^2-25(x-2)^2=0
The zeros of 4(x-3)^2-25(x-2)^2=0 are x= 4/3 ,x= 16/7