Solve (8x^(2) 4)-(2x^(2)-5-5x)

Question

Simplify the expression

30 x^{2} + 5 + 5 x

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5 (6 x^{2} + 1 + x)

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x_{1} = - \frac{1}{12} - \frac{23}{12} i, x_{2} = - \frac{1}{12} + \frac{23}{12} i

Alternative Form

x_{1} \approx - 0.08 \dot{3} - 0.399653 i, x_{2} \approx - 0.08 \dot{3} + 0.399653 i

Evaluate

(8 x^{2} \times 4) - (2 x^{2} - 5 - 5 x)

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

(8 x^{2} \times 4) - (2 x^{2} - 5 - 5 x) = 0

Multiply the terms

32 x^{2} - (2 x^{2} - 5 - 5 x) = 0

Subtract the terms

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

Rewrite in standard form

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

Substitute a= 30,b= 5 and c= 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 \times 30 \times 5}{2 \times 30}

Simplify the expression

x = \frac{- 5 \pm 5 ^{2} - 4 \times 30 \times 5}{60}

Simplify the expression

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x = \frac{- 5 \pm - 575}{60}

Simplify the radical expression

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x = \frac{- 5 \pm 5 23 \times i}{60}

Separate the equation into 2 possible cases

x = \frac{- 5 + 5 23 \times i}{60} x = \frac{- 5 - 5 23 \times i}{60}

Simplify the expression

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x = - \frac{1}{12} + \frac{23}{12} i x = \frac{- 5 - 5 23 \times i}{60}

Simplify the expression

More Steps

x = - \frac{1}{12} + \frac{23}{12} i x = - \frac{1}{12} - \frac{23}{12} i

Solution

x_{1} = - \frac{1}{12} - \frac{23}{12} i, x_{2} = - \frac{1}{12} + \frac{23}{12} i

Alternative Form

x_{1} \approx - 0.08 \dot{3} - 0.399653 i, x_{2} \approx - 0.08 \dot{3} + 0.399653 i

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