Solve 4x-102x 77x-25=180

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}{3927} - \frac{1610066}{7854} i, x_{2} = \frac{1}{3927} + \frac{1610066}{7854} i

Alternative Form

x_{1} \approx 0.000255 - 0.161559 i, x_{2} \approx 0.000255 + 0.161559 i

Evaluate

4 x - 102 x \times 77 x - 25 = 180

Multiply

More Steps

4 x - 7854 x^{2} - 25 = 180

Move the expression to the left side

4 x - 7854 x^{2} - 205 = 0

Rewrite in standard form

- 7854 x^{2} + 4 x - 205 = 0

Multiply both sides

7854 x^{2} - 4 x + 205 = 0

Substitute a= 7854,b= - 4 and c= 205 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 7854 \times 205}{2 \times 7854}

Simplify the expression

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 7854 \times 205}{15708}

Simplify the expression

More Steps

x = \frac{4 \pm - 6440264}{15708}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 1610066 \times i}{15708}

Separate the equation into 2 possible cases

x = \frac{4 + 2 1610066 \times i}{15708} x = \frac{4 - 2 1610066 \times i}{15708}

Simplify the expression

More Steps

x = \frac{1}{3927} + \frac{1610066}{7854} i x = \frac{4 - 2 1610066 \times i}{15708}

Simplify the expression

More Steps

x = \frac{1}{3927} + \frac{1610066}{7854} i x = \frac{1}{3927} - \frac{1610066}{7854} i

Solution

x_{1} = \frac{1}{3927} - \frac{1610066}{7854} i, x_{2} = \frac{1}{3927} + \frac{1610066}{7854} i

Alternative Form

x_{1} \approx 0.000255 - 0.161559 i, x_{2} \approx 0.000255 + 0.161559 i

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