Solve -5x - 25 = 5x^25

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}{10} - \frac{3 11}{10} i, x_{2} = - \frac{1}{10} + \frac{3 11}{10} i

Alternative Form

x_{1} \approx - 0.1 - 0.994987 i, x_{2} \approx - 0.1 + 0.994987 i

Evaluate

- 5 x - 25 = 5 x^{2} \times 5

Multiply the terms

- 5 x - 25 = 25 x^{2}

Swap the sides

25 x^{2} = - 5 x - 25

Move the expression to the left side

25 x^{2} + 5 x + 25 = 0

Substitute a= 25,b= 5 and c= 25 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 \times 25 \times 25}{2 \times 25}

Simplify the expression

x = \frac{- 5 \pm 5 ^{2} - 4 \times 25 \times 25}{50}

Simplify the expression

More Steps

x = \frac{- 5 \pm - 2475}{50}

Simplify the radical expression

More Steps

x = \frac{- 5 \pm 15 11 \times i}{50}

Separate the equation into 2 possible cases

x = \frac{- 5 + 15 11 \times i}{50} x = \frac{- 5 - 15 11 \times i}{50}

Simplify the expression

More Steps

x = - \frac{1}{10} + \frac{3 11}{10} i x = \frac{- 5 - 15 11 \times i}{50}

Simplify the expression

More Steps

x = - \frac{1}{10} + \frac{3 11}{10} i x = - \frac{1}{10} - \frac{3 11}{10} i

Solution

x_{1} = - \frac{1}{10} - \frac{3 11}{10} i, x_{2} = - \frac{1}{10} + \frac{3 11}{10} i

Alternative Form

x_{1} \approx - 0.1 - 0.994987 i, x_{2} \approx - 0.1 + 0.994987 i

Show Solution