What are the solutions to the equation (x+3)^2+(x-1)^2=45 ?

The solutions to the equation (x+3)^2+(x-1)^2=45 are x=(-2+sqrt(74))/2 ,x=-(2+sqrt(74))/2

Find the zeros of (x+3)^2+(x-1)^2=45

The zeros of (x+3)^2+(x-1)^2=45 are x=(-2+sqrt(74))/2 ,x=-(2+sqrt(74))/2

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(x + 3)^{2} + (x - 1)^{2} = 45

x = \frac{- 2 + 74}{2}, x = - \frac{2 + 74}{2}

Decimal Notation

x = 3.30116 \dots, x = - 5.30116 \dots

Solution steps

(x + 3)^{2} + (x - 1)^{2} = 45

Expand

(x + 3)^{2} + (x - 1)^{2} : 2 x^{2} + 4 x + 10

2 x^{2} + 4 x + 10 = 45

Move

45

to the left side

2 x^{2} + 4 x - 35 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 2 ( - 35 )}{2 \cdot 2}

4^{2} - 4 \cdot 2 (- 35) = 274

x_{1, 2} = \frac{- 4 \pm 2 74}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 4 + 2 74}{2 \cdot 2}, x_{2} = \frac{- 4 - 2 74}{2 \cdot 2}

x = \frac{- 4 + 2 74}{2 \cdot 2} : \frac{- 2 + 74}{2}

x = \frac{- 4 - 2 74}{2 \cdot 2} : - \frac{2 + 74}{2}

The solutions to the quadratic equation are:

x = \frac{- 2 + 74}{2}, x = - \frac{2 + 74}{2}

\frac{1}{2} x^{2} = 8

3 - x = 3 - x^{2}

x^{2} + 9 x + c

x, 3 x^{2} + 10 x - 5 = 0

4 x^{2} - 32 x = - 60

What are the solutions to the equation (x+3)^2+(x-1)^2=45 ?
The solutions to the equation (x+3)^2+(x-1)^2=45 are x=(-2+sqrt(74))/2 ,x=-(2+sqrt(74))/2
Find the zeros of (x+3)^2+(x-1)^2=45
The zeros of (x+3)^2+(x-1)^2=45 are x=(-2+sqrt(74))/2 ,x=-(2+sqrt(74))/2