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

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

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

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

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x (x + 3) = - 1

x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Decimal Notation

x = - 0.38196 \dots, x = - 2.61803 \dots

Solution steps

x (x + 3) = - 1

Expand

x (x + 3) : x^{2} + 3 x

x^{2} + 3 x = - 1

Move

1

to the left side

x^{2} + 3 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

3^{2} - 4 \cdot 1 \cdot 1 = 5

x_{1, 2} = \frac{- 3 \pm 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 3 + 5}{2 \cdot 1}, x_{2} = \frac{- 3 - 5}{2 \cdot 1}

x = \frac{- 3 + 5}{2 \cdot 1} : \frac{- 3 + 5}{2}

x = \frac{- 3 - 5}{2 \cdot 1} : \frac{- 3 - 5}{2}

The solutions to the quadratic equation are:

x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

4 x^{2} + 6 x - 28 = 0

(x + 5) (x - 5) = 3 x - 2

0 = 5 x^{2} + 15

4 (x - 6)^{2} - 5 = 319

2 x^{2} - 14 x + 1 = 0

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