What are the solutions to the equation (x+9)^2=(x+1)^2+x^2 ?

The solutions to the equation (x+9)^2=(x+1)^2+x^2 are x=-4,x=20

Find the zeros of (x+9)^2=(x+1)^2+x^2

The zeros of (x+9)^2=(x+1)^2+x^2 are x=-4,x=20

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(x + 9)^{2} = (x + 1)^{2} + x^{2}

x = - 4, x = 20

Solution steps

(x + 9)^{2} = (x + 1)^{2} + x^{2}

Expand

(x + 9)^{2} : x^{2} + 18 x + 81

Expand

(x + 1)^{2} + x^{2} : 2 x^{2} + 2 x + 1

x^{2} + 18 x + 81 = 2 x^{2} + 2 x + 1

Move

1

to the left side

x^{2} + 18 x + 80 = 2 x^{2} + 2 x

Move

2 x

to the left side

x^{2} + 16 x + 80 = 2 x^{2}

Move

2 x^{2}

to the left side

- x^{2} + 16 x + 80 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 ( - 1 ) \cdot 80}{2 ( - 1 )}

1 6^{2} - 4 (- 1) \cdot 80 = 24

x_{1, 2} = \frac{- 16 \pm 24}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 16 + 24}{2 ( - 1 )}, x_{2} = \frac{- 16 - 24}{2 ( - 1 )}

x = \frac{- 16 + 24}{2 ( - 1 )} : - 4

x = \frac{- 16 - 24}{2 ( - 1 )} : 20

The solutions to the quadratic equation are:

x = - 4, x = 20

x^{2} + 11 x + 24 = 0

80000 = 100 - 6.25 (x - 9)^{2}

t (t + 1) = 3 t^{2} + 1

3 b^{2} = 12

5 x = 18 - x^{2} - 2 x

What are the solutions to the equation (x+9)^2=(x+1)^2+x^2 ?
The solutions to the equation (x+9)^2=(x+1)^2+x^2 are x=-4,x=20
Find the zeros of (x+9)^2=(x+1)^2+x^2
The zeros of (x+9)^2=(x+1)^2+x^2 are x=-4,x=20