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

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

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

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

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

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

Solution steps

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

Expand

(x + 3)^{2} : x^{2} + 6 x + 9

x^{2} + 6 x + 9 = 3 x

Move

3 x

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 1 \cdot 9}{2 \cdot 1}

Simplify

3^{2} - 4 \cdot 1 \cdot 9 : 33 i

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

x^{2} + 7^{2} = 9^{2}

x^{2} + x - 6 = 0

x^{2} = x + 42

- 5 x^{2} + 6 x + 2 = 0

9 x^{2} = - 9 x + 40

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