What are the solutions to the equation 0.5x^2+3x=-3 ?

The solutions to the equation 0.5x^2+3x=-3 are x=-3+sqrt(3),x=-3-sqrt(3)

Find the zeros of 0.5x^2+3x=-3

The zeros of 0.5x^2+3x=-3 are x=-3+sqrt(3),x=-3-sqrt(3)

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

x = - 3 + 3, x = - 3 - 3

Decimal Notation

x = - 1.26794 \dots, x = - 4.73205 \dots

Solution steps

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

Multiply both sides by

10

5 x^{2} + 30 x = - 30

Move

30

to the left side

5 x^{2} + 30 x + 30 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 30 \pm 3 0 ^{2} - 4 \cdot 5 \cdot 30}{2 \cdot 5}

3 0^{2} - 4 \cdot 5 \cdot 30 = 103

x_{1, 2} = \frac{- 30 \pm 10 3}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- 30 + 10 3}{2 \cdot 5}, x_{2} = \frac{- 30 - 10 3}{2 \cdot 5}

x = \frac{- 30 + 10 3}{2 \cdot 5} : - 3 + 3

x = \frac{- 30 - 10 3}{2 \cdot 5} : - 3 - 3

The solutions to the quadratic equation are:

x = - 3 + 3, x = - 3 - 3

5 x^{2} + 5 = 26 x

4 x^{2} - 21 x - 49 = 0

p^{2} - 2 p - 91 = 8

\frac{1}{2} A = π x^{2}

4 x^{2} + 36 x = 0

What are the solutions to the equation 0.5x^2+3x=-3 ?
The solutions to the equation 0.5x^2+3x=-3 are x=-3+sqrt(3),x=-3-sqrt(3)
Find the zeros of 0.5x^2+3x=-3
The zeros of 0.5x^2+3x=-3 are x=-3+sqrt(3),x=-3-sqrt(3)