Solve 6a^2-3a-96a^2-3a-9

Question

Simplify the expression

- 90 a^{2} - 6 a - 9

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- 3 (30 a^{2} + 2 a + 3)

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a_{1} = - \frac{1}{30} - \frac{89}{30} i, a_{2} = - \frac{1}{30} + \frac{89}{30} i

Alternative Form

a_{1} \approx - 0.0 \dot{3} - 0.314466 i, a_{2} \approx - 0.0 \dot{3} + 0.314466 i

Evaluate

6 a^{2} - 3 a - 96 a^{2} - 3 a - 9

To find the roots of the expression,set the expression equal to 0

6 a^{2} - 3 a - 96 a^{2} - 3 a - 9 = 0

Subtract the terms

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- 90 a^{2} - 3 a - 3 a - 9 = 0

Subtract the terms

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- 90 a^{2} - 6 a - 9 = 0

Multiply both sides

90 a^{2} + 6 a + 9 = 0

Substitute a= 90,b= 6 and c= 9 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{- 6 \pm 6 ^{2} - 4 \times 90 \times 9}{2 \times 90}

Simplify the expression

a = \frac{- 6 \pm 6 ^{2} - 4 \times 90 \times 9}{180}

Simplify the expression

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a = \frac{- 6 \pm - 3204}{180}

Simplify the radical expression

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a = \frac{- 6 \pm 6 89 \times i}{180}

Separate the equation into 2 possible cases

a = \frac{- 6 + 6 89 \times i}{180} a = \frac{- 6 - 6 89 \times i}{180}

Simplify the expression

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a = - \frac{1}{30} + \frac{89}{30} i a = \frac{- 6 - 6 89 \times i}{180}

Simplify the expression

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a = - \frac{1}{30} + \frac{89}{30} i a = - \frac{1}{30} - \frac{89}{30} i

Solution

a_{1} = - \frac{1}{30} - \frac{89}{30} i, a_{2} = - \frac{1}{30} + \frac{89}{30} i

Alternative Form

a_{1} \approx - 0.0 \dot{3} - 0.314466 i, a_{2} \approx - 0.0 \dot{3} + 0.314466 i

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