What are the solutions to the equation x(x+6)+2x(x+4)=x^2+8 ?

The solutions to the equation x(x+6)+2x(x+4)=x^2+8 are x=(-7+sqrt(65))/2 ,x=-(7+sqrt(65))/2

Find the zeros of x(x+6)+2x(x+4)=x^2+8

The zeros of x(x+6)+2x(x+4)=x^2+8 are x=(-7+sqrt(65))/2 ,x=-(7+sqrt(65))/2

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x (x + 6) + 2 x (x + 4) = x^{2} + 8

x = \frac{- 7 + 65}{2}, x = - \frac{7 + 65}{2}

Decimal Notation

x = 0.53112 \dots, x = - 7.53112 \dots

Solution steps

x (x + 6) + 2 x (x + 4) = x^{2} + 8

Expand

x (x + 6) + 2 x (x + 4) : 3 x^{2} + 14 x

3 x^{2} + 14 x = x^{2} + 8

Move

8

to the left side

3 x^{2} + 14 x - 8 = x^{2}

Move

x^{2}

to the left side

2 x^{2} + 14 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 14 \pm 1 4 ^{2} - 4 \cdot 2 ( - 8 )}{2 \cdot 2}

1 4^{2} - 4 \cdot 2 (- 8) = 265

x_{1, 2} = \frac{- 14 \pm 2 65}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- 14 + 2 65}{2 \cdot 2}, x_{2} = \frac{- 14 - 2 65}{2 \cdot 2}

x = \frac{- 14 + 2 65}{2 \cdot 2} : \frac{- 7 + 65}{2}

x = \frac{- 14 - 2 65}{2 \cdot 2} : - \frac{7 + 65}{2}

The solutions to the quadratic equation are:

x = \frac{- 7 + 65}{2}, x = - \frac{7 + 65}{2}

- 0.2 q^{2} + 80 = 4 q + 20

4 x - 16 = - 2 x^{2}

10 - 2 x^{2} = 0

x^{2} - 23 x + 4 = 0

8 x - 3 = 2 x^{2} + 3

What are the solutions to the equation x(x+6)+2x(x+4)=x^2+8 ?
The solutions to the equation x(x+6)+2x(x+4)=x^2+8 are x=(-7+sqrt(65))/2 ,x=-(7+sqrt(65))/2
Find the zeros of x(x+6)+2x(x+4)=x^2+8
The zeros of x(x+6)+2x(x+4)=x^2+8 are x=(-7+sqrt(65))/2 ,x=-(7+sqrt(65))/2