Solve -2(x-6)=-4x^24

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

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Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{1}{16} - \frac{191}{16} i, x_{2} = \frac{1}{16} + \frac{191}{16} i

Alternative Form

x_{1} \approx 0.0625 - 0.863767 i, x_{2} \approx 0.0625 + 0.863767 i

Evaluate

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

Multiply the terms

- 2 (x - 6) = - 16 x^{2}

Swap the sides

- 16 x^{2} = - 2 (x - 6)

Expand the expression

More Steps

- 16 x^{2} = - 2 x + 12

Move the expression to the left side

- 16 x^{2} + 2 x - 12 = 0

Multiply both sides

16 x^{2} - 2 x + 12 = 0

Substitute a= 16,b= - 2 and c= 12 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 16 \times 12}{2 \times 16}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 16 \times 12}{32}

Simplify the expression

More Steps

x = \frac{2 \pm - 764}{32}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 191 \times i}{32}

Separate the equation into 2 possible cases

x = \frac{2 + 2 191 \times i}{32} x = \frac{2 - 2 191 \times i}{32}

Simplify the expression

More Steps

x = \frac{1}{16} + \frac{191}{16} i x = \frac{2 - 2 191 \times i}{32}

Simplify the expression

More Steps

x = \frac{1}{16} + \frac{191}{16} i x = \frac{1}{16} - \frac{191}{16} i

Solution

x_{1} = \frac{1}{16} - \frac{191}{16} i, x_{2} = \frac{1}{16} + \frac{191}{16} i

Alternative Form

x_{1} \approx 0.0625 - 0.863767 i, x_{2} \approx 0.0625 + 0.863767 i

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