What are the solutions to the equation (x+5)^2+5(2x+3)=2(x+4)^2 ?

The solutions to the equation (x+5)^2+5(2x+3)=2(x+4)^2 are x=-2(sqrt(3)-1),x=2(1+sqrt(3))

Find the zeros of (x+5)^2+5(2x+3)=2(x+4)^2

The zeros of (x+5)^2+5(2x+3)=2(x+4)^2 are x=-2(sqrt(3)-1),x=2(1+sqrt(3))

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(x + 5)^{2} + 5 (2 x + 3) = 2 (x + 4)^{2}

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

Decimal Notation

x = - 1.46410 \dots, x = 5.46410 \dots

Solution steps

(x + 5)^{2} + 5 (2 x + 3) = 2 (x + 4)^{2}

Expand

(x + 5)^{2} + 5 (2 x + 3) : x^{2} + 20 x + 40

Expand

2 (x + 4)^{2} : 2 x^{2} + 16 x + 32

x^{2} + 20 x + 40 = 2 x^{2} + 16 x + 32

Move

32

to the left side

x^{2} + 20 x + 8 = 2 x^{2} + 16 x

Move

16 x

to the left side

x^{2} + 4 x + 8 = 2 x^{2}

Move

2 x^{2}

to the left side

- x^{2} + 4 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 ( - 1 ) \cdot 8}{2 ( - 1 )}

4^{2} - 4 (- 1) \cdot 8 = 43

x_{1, 2} = \frac{- 4 \pm 4 3}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 4 + 4 3}{2 ( - 1 )}, x_{2} = \frac{- 4 - 4 3}{2 ( - 1 )}

x = \frac{- 4 + 4 3}{2 ( - 1 )} : - 2 (3 - 1)

x = \frac{- 4 - 4 3}{2 ( - 1 )} : 2 (1 + 3)

The solutions to the quadratic equation are:

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

4 x^{2} + 40 x + 100 = 0

x^{2} - 8 x + 96 = 0

x, 3 x^{2} - 5 y^{6} = 2 x

2 (3 x + 1)^{2} - 8 = 0

9 x^{2} - 18 x + 3 = 0

What are the solutions to the equation (x+5)^2+5(2x+3)=2(x+4)^2 ?
The solutions to the equation (x+5)^2+5(2x+3)=2(x+4)^2 are x=-2(sqrt(3)-1),x=2(1+sqrt(3))
Find the zeros of (x+5)^2+5(2x+3)=2(x+4)^2
The zeros of (x+5)^2+5(2x+3)=2(x+4)^2 are x=-2(sqrt(3)-1),x=2(1+sqrt(3))