What are the solutions to the equation 100x^2-250(x-3)^2-700=0 ?

The solutions to the equation 100x^2-250(x-3)^2-700=0 are x=(15-4sqrt(3))/3 ,x=(15+4sqrt(3))/3

Find the zeros of 100x^2-250(x-3)^2-700=0

The zeros of 100x^2-250(x-3)^2-700=0 are x=(15-4sqrt(3))/3 ,x=(15+4sqrt(3))/3

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100 x^{2} - 250 (x - 3)^{2} - 700 = 0

x = \frac{15 - 4 3}{3}, x = \frac{15 + 4 3}{3}

Decimal Notation

x = 2.69059 \dots, x = 7.30940 \dots

Solution steps

100 x^{2} - 250 (x - 3)^{2} - 700 = 0

Expand

100 x^{2} - 250 (x - 3)^{2} - 700 : - 150 x^{2} + 1500 x - 2950

- 150 x^{2} + 1500 x - 2950 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1500 \pm 150 0 ^{2} - 4 ( - 150 ) ( - 2950 )}{2 ( - 150 )}

150 0^{2} - 4 (- 150) (- 2950) = 4003

x_{1, 2} = \frac{- 1500 \pm 400 3}{2 ( - 150 )}

Separate the solutions

x_{1} = \frac{- 1500 + 400 3}{2 ( - 150 )}, x_{2} = \frac{- 1500 - 400 3}{2 ( - 150 )}

x = \frac{- 1500 + 400 3}{2 ( - 150 )} : \frac{15 - 4 3}{3}

x = \frac{- 1500 - 400 3}{2 ( - 150 )} : \frac{15 + 4 3}{3}

The solutions to the quadratic equation are:

x = \frac{15 - 4 3}{3}, x = \frac{15 + 4 3}{3}

x, y = f (x^{2})

5 X^{2} - 15 X - 50 = 0

(x + 2) (x - 4) = x + 2

(x - 5)^{2} + 2 = 0

(3 x - 1) (2 x + 3) = 0

What are the solutions to the equation 100x^2-250(x-3)^2-700=0 ?
The solutions to the equation 100x^2-250(x-3)^2-700=0 are x=(15-4sqrt(3))/3 ,x=(15+4sqrt(3))/3
Find the zeros of 100x^2-250(x-3)^2-700=0
The zeros of 100x^2-250(x-3)^2-700=0 are x=(15-4sqrt(3))/3 ,x=(15+4sqrt(3))/3