What are the solutions to the equation 9x^2=-54x-83 ?

The solutions to the equation 9x^2=-54x-83 are x=-3+i(sqrt(2))/3 ,x=-3-i(sqrt(2))/3

Find the zeros of 9x^2=-54x-83

The zeros of 9x^2=-54x-83 are x=-3+i(sqrt(2))/3 ,x=-3-i(sqrt(2))/3

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9 x^{2} = - 54 x - 83

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

Solution steps

9 x^{2} = - 54 x - 83

Move

83

to the left side

9 x^{2} + 83 = - 54 x

Move

54 x

to the left side

9 x^{2} + 83 + 54 x = 0

Write in the standard form

a x^{2} + b x + c = 0

9 x^{2} + 54 x + 83 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 54 \pm 5 4 ^{2} - 4 \cdot 9 \cdot 83}{2 \cdot 9}

Simplify

5 4^{2} - 4 \cdot 9 \cdot 83 : 62 i

x_{1, 2} = \frac{- 54 \pm 6 2 i}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- 54 + 6 2 i}{2 \cdot 9}, x_{2} = \frac{- 54 - 6 2 i}{2 \cdot 9}

x = \frac{- 54 + 6 2 i}{2 \cdot 9} : - 3 + i \frac{2}{3}

x = \frac{- 54 - 6 2 i}{2 \cdot 9} : - 3 - i \frac{2}{3}

The solutions to the quadratic equation are:

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

a^{2} - 10 a = - 24

x^{2} + 9 x - 52 = 0

∣ 2 a + 7 ∣ = ∣ 3 a - 7 ∣

x^{2} \geq 5 x - 6

\frac{1}{2} \leq \frac{1 - 2 t}{3} < \frac{2}{3}

What are the solutions to the equation 9x^2=-54x-83 ?
The solutions to the equation 9x^2=-54x-83 are x=-3+i(sqrt(2))/3 ,x=-3-i(sqrt(2))/3
Find the zeros of 9x^2=-54x-83
The zeros of 9x^2=-54x-83 are x=-3+i(sqrt(2))/3 ,x=-3-i(sqrt(2))/3