Solve -3(-2x-2)-2x^2=28

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{3}{2} - \frac{35}{2} i, x_{2} = \frac{3}{2} + \frac{35}{2} i

Alternative Form

x_{1} \approx 1.5 - 2.95804 i, x_{2} \approx 1.5 + 2.95804 i

Evaluate

- 3 (- 2 x - 2) - 2 x^{2} = 28

Expand the expression

More Steps

6 x + 6 - 2 x^{2} = 28

Move the expression to the left side

6 x - 22 - 2 x^{2} = 0

Rewrite in standard form

- 2 x^{2} + 6 x - 22 = 0

Multiply both sides

2 x^{2} - 6 x + 22 = 0

Substitute a= 2,b= - 6 and c= 22 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 2 \times 22}{2 \times 2}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 2 \times 22}{4}

Simplify the expression

More Steps

x = \frac{6 \pm - 140}{4}

Simplify the radical expression

More Steps

x = \frac{6 \pm 2 35 \times i}{4}

Separate the equation into 2 possible cases

x = \frac{6 + 2 35 \times i}{4} x = \frac{6 - 2 35 \times i}{4}

Simplify the expression

More Steps

x = \frac{3}{2} + \frac{35}{2} i x = \frac{6 - 2 35 \times i}{4}

Simplify the expression

More Steps

x = \frac{3}{2} + \frac{35}{2} i x = \frac{3}{2} - \frac{35}{2} i

Solution

x_{1} = \frac{3}{2} - \frac{35}{2} i, x_{2} = \frac{3}{2} + \frac{35}{2} i

Alternative Form

x_{1} \approx 1.5 - 2.95804 i, x_{2} \approx 1.5 + 2.95804 i

Show Solution