What are the solutions to the equation completesquare 25(x+2)^2=(x-7)^2-81 ?

The solutions to the equation completesquare 25(x+2)^2=(x-7)^2-81 are x=-2,x=-11/4

Find the zeros of completesquare 25(x+2)^2=(x-7)^2-81

The zeros of completesquare 25(x+2)^2=(x-7)^2-81 are x=-2,x=-11/4

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25 (x + 2)^{2} = (x - 7)^{2} - 81

x = - 2, x = - \frac{11}{4}

Solution steps

25 (x + 2)^{2} = (x - 7)^{2} - 81

Expand

25 (x + 2)^{2} : 25 x^{2} + 100 x + 100

Expand

(x - 7)^{2} - 81 : x^{2} - 14 x - 32

25 x^{2} + 100 x + 100 = x^{2} - 14 x - 32

Move

100

to the right side

25 x^{2} + 100 x = x^{2} - 14 x - 132

Move

14 x

to the left side

25 x^{2} + 114 x = x^{2} - 132

Move

x^{2}

to the left side

24 x^{2} + 114 x = - 132

Divide both sides by

24

\frac{24 x ^{2} + 114 x}{24} = \frac{- 132}{24}

x^{2} + \frac{19 x}{4} = - \frac{11}{2}

Rewrite in the form

(x + a)^{2} = b

(x + \frac{19}{8})^{2} = \frac{9}{64}

For

the solutions are

f (x) = a, - a

Solve

x + \frac{19}{8} = \frac{9}{64} : x = - 2

Solve

x + \frac{19}{8} = - \frac{9}{64} : x = - \frac{11}{4}

The solutions to the quadratic equation are:

x = - 2, x = - \frac{11}{4}

k^{2} - 4 k + 1 = - 19

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

(2 x + 3)^{2} = (x + 4) (x + 3)

9 x - 8 = x^{2}

x, y^{3} + 3 y^{2} - 9 y = x^{2} + 10 x + 12

What are the solutions to the equation completesquare 25(x+2)^2=(x-7)^2-81 ?
The solutions to the equation completesquare 25(x+2)^2=(x-7)^2-81 are x=-2,x=-11/4
Find the zeros of completesquare 25(x+2)^2=(x-7)^2-81
The zeros of completesquare 25(x+2)^2=(x-7)^2-81 are x=-2,x=-11/4