Solve -17p-p-14p 11p-1=20

Question

Solve the equation(The real numbers system)

p \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

p_{1} = - \frac{9}{154} - \frac{3153}{154} i, p_{2} = - \frac{9}{154} + \frac{3153}{154} i

Alternative Form

p_{1} \approx - 0.0 \dot{5} 8441 \dot{5} - 0.364621 i, p_{2} \approx - 0.0 \dot{5} 8441 \dot{5} + 0.364621 i

Evaluate

- 17 p - p - 14 p \times 11 p - 1 = 20

Simplify

More Steps

- 18 p - 154 p^{2} - 1 = 20

Move the expression to the left side

- 18 p - 154 p^{2} - 21 = 0

Rewrite in standard form

- 154 p^{2} - 18 p - 21 = 0

Multiply both sides

154 p^{2} + 18 p + 21 = 0

Substitute a= 154,b= 18 and c= 21 into the quadratic formula p = \frac{- b \pm b ^{2} - 4 a c}{2 a}

p = \frac{- 18 \pm 1 8 ^{2} - 4 \times 154 \times 21}{2 \times 154}

Simplify the expression

p = \frac{- 18 \pm 1 8 ^{2} - 4 \times 154 \times 21}{308}

Simplify the expression

More Steps

p = \frac{- 18 \pm - 12612}{308}

Simplify the radical expression

More Steps

p = \frac{- 18 \pm 2 3153 \times i}{308}

Separate the equation into 2 possible cases

p = \frac{- 18 + 2 3153 \times i}{308} p = \frac{- 18 - 2 3153 \times i}{308}

Simplify the expression

More Steps

p = - \frac{9}{154} + \frac{3153}{154} i p = \frac{- 18 - 2 3153 \times i}{308}

Simplify the expression

More Steps

p = - \frac{9}{154} + \frac{3153}{154} i p = - \frac{9}{154} - \frac{3153}{154} i

Solution

p_{1} = - \frac{9}{154} - \frac{3153}{154} i, p_{2} = - \frac{9}{154} + \frac{3153}{154} i

Alternative Form

p_{1} \approx - 0.0 \dot{5} 8441 \dot{5} - 0.364621 i, p_{2} \approx - 0.0 \dot{5} 8441 \dot{5} + 0.364621 i

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