What are the solutions to the equation (x-9)^2+(x+3)^2=10x+54 ?

The solutions to the equation (x-9)^2+(x+3)^2=10x+54 are x=9,x=2

Find the zeros of (x-9)^2+(x+3)^2=10x+54

The zeros of (x-9)^2+(x+3)^2=10x+54 are x=9,x=2

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(x - 9)^{2} + (x + 3)^{2} = 10 x + 54

x = 9, x = 2

Solution steps

(x - 9)^{2} + (x + 3)^{2} = 10 x + 54

Expand

(x - 9)^{2} + (x + 3)^{2} : 2 x^{2} - 12 x + 90

2 x^{2} - 12 x + 90 = 10 x + 54

Move

54

to the left side

2 x^{2} - 12 x + 36 = 10 x

Move

10 x

to the left side

2 x^{2} - 22 x + 36 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 22 ) \pm ( - 22 ) ^{2} - 4 \cdot 2 \cdot 36}{2 \cdot 2}

(- 22)^{2} - 4 \cdot 2 \cdot 36 = 14

x_{1, 2} = \frac{- ( - 22 ) \pm 14}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 22 ) + 14}{2 \cdot 2}, x_{2} = \frac{- ( - 22 ) - 14}{2 \cdot 2}

x = \frac{- ( - 22 ) + 14}{2 \cdot 2} : 9

x = \frac{- ( - 22 ) - 14}{2 \cdot 2} : 2

The solutions to the quadratic equation are:

x = 9, x = 2

10 x^{2} - 100 = 0

5 y^{2} - 30 y - 18 = 0

4 x^{2} - 8 x - 294 = - 10

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

3 x^{2} + 9 x + 12 = 0

What are the solutions to the equation (x-9)^2+(x+3)^2=10x+54 ?
The solutions to the equation (x-9)^2+(x+3)^2=10x+54 are x=9,x=2
Find the zeros of (x-9)^2+(x+3)^2=10x+54
The zeros of (x-9)^2+(x+3)^2=10x+54 are x=9,x=2