Solve 3(2x^(2) 4)-4(x-6)

Question

Simplify the expression

24 x^{2} - 4 x + 24

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4 (6 x^{2} - x + 6)

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x_{1} = \frac{1}{12} - \frac{143}{12} i, x_{2} = \frac{1}{12} + \frac{143}{12} i

Alternative Form

x_{1} \approx 0.08 \dot{3} - 0.996522 i, x_{2} \approx 0.08 \dot{3} + 0.996522 i

Evaluate

3 (2 x^{2} \times 4) - 4 (x - 6)

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

3 (2 x^{2} \times 4) - 4 (x - 6) = 0

Multiply the terms

3 \times 8 x^{2} - 4 (x - 6) = 0

Multiply the numbers

24 x^{2} - 4 (x - 6) = 0

Calculate

More Steps

24 x^{2} - 4 x + 24 = 0

Substitute a= 24,b= - 4 and c= 24 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 24 \times 24}{2 \times 24}

Simplify the expression

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 24 \times 24}{48}

Simplify the expression

More Steps

x = \frac{4 \pm - 2288}{48}

Simplify the radical expression

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x = \frac{4 \pm 4 143 \times i}{48}

Separate the equation into 2 possible cases

x = \frac{4 + 4 143 \times i}{48} x = \frac{4 - 4 143 \times i}{48}

Simplify the expression

More Steps

x = \frac{1}{12} + \frac{143}{12} i x = \frac{4 - 4 143 \times i}{48}

Simplify the expression

More Steps

x = \frac{1}{12} + \frac{143}{12} i x = \frac{1}{12} - \frac{143}{12} i

Solution

x_{1} = \frac{1}{12} - \frac{143}{12} i, x_{2} = \frac{1}{12} + \frac{143}{12} i

Alternative Form

x_{1} \approx 0.08 \dot{3} - 0.996522 i, x_{2} \approx 0.08 \dot{3} + 0.996522 i

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