Solve 7w-2(w-9)=4-8(w^2)

Question

Solve the equation(The real numbers system)

w \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

w_{1} = - \frac{5}{16} - \frac{3 47}{16} i, w_{2} = - \frac{5}{16} + \frac{3 47}{16} i

Alternative Form

w_{1} \approx - 0.3125 - 1.285435 i, w_{2} \approx - 0.3125 + 1.285435 i

Evaluate

7 w - 2 (w - 9) = 4 - 8 w^{2}

Swap the sides

4 - 8 w^{2} = 7 w - 2 (w - 9)

Expand the expression

More Steps

4 - 8 w^{2} = 5 w + 18

Move the expression to the left side

- 14 - 8 w^{2} - 5 w = 0

Rewrite in standard form

- 8 w^{2} - 5 w - 14 = 0

Multiply both sides

8 w^{2} + 5 w + 14 = 0

Substitute a= 8,b= 5 and c= 14 into the quadratic formula w = \frac{- b \pm b ^{2} - 4 a c}{2 a}

w = \frac{- 5 \pm 5 ^{2} - 4 \times 8 \times 14}{2 \times 8}

Simplify the expression

w = \frac{- 5 \pm 5 ^{2} - 4 \times 8 \times 14}{16}

Simplify the expression

More Steps

w = \frac{- 5 \pm - 423}{16}

Simplify the radical expression

More Steps

w = \frac{- 5 \pm 3 47 \times i}{16}

Separate the equation into 2 possible cases

w = \frac{- 5 + 3 47 \times i}{16} w = \frac{- 5 - 3 47 \times i}{16}

Simplify the expression

More Steps

w = - \frac{5}{16} + \frac{3 47}{16} i w = \frac{- 5 - 3 47 \times i}{16}

Simplify the expression

More Steps

w = - \frac{5}{16} + \frac{3 47}{16} i w = - \frac{5}{16} - \frac{3 47}{16} i

Solution

w_{1} = - \frac{5}{16} - \frac{3 47}{16} i, w_{2} = - \frac{5}{16} + \frac{3 47}{16} i

Alternative Form

w_{1} \approx - 0.3125 - 1.285435 i, w_{2} \approx - 0.3125 + 1.285435 i

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