Solve (x^2-4x-12)-(5x^2-2)

Question

Simplify the expression

- 4 x^{2} - 4 x - 10

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- 2 (2 x^{2} + 2 x + 5)

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

Alternative Form

x_{1} = - 0.5 - 1.5 i, x_{2} = - 0.5 + 1.5 i

Evaluate

(x^{2} - 4 x - 12) - (5 x^{2} - 2)

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

(x^{2} - 4 x - 12) - (5 x^{2} - 2) = 0

Remove the parentheses

x^{2} - 4 x - 12 - (5 x^{2} - 2) = 0

Subtract the terms

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- 4 x^{2} - 4 x - 10 = 0

Multiply both sides

4 x^{2} + 4 x + 10 = 0

Substitute a= 4,b= 4 and c= 10 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 4 \pm 4 ^{2} - 4 \times 4 \times 10}{2 \times 4}

Simplify the expression

x = \frac{- 4 \pm 4 ^{2} - 4 \times 4 \times 10}{8}

Simplify the expression

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x = \frac{- 4 \pm - 144}{8}

Simplify the radical expression

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x = \frac{- 4 \pm 12 i}{8}

Separate the equation into 2 possible cases

x = \frac{- 4 + 12 i}{8} x = \frac{- 4 - 12 i}{8}

Simplify the expression

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x = - \frac{1}{2} + \frac{3}{2} i x = \frac{- 4 - 12 i}{8}

Simplify the expression

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

Solution

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

Alternative Form

x_{1} = - 0.5 - 1.5 i, x_{2} = - 0.5 + 1.5 i

Show Solution