Solve (5x+6)^2 + (13x-2)^2 = 0

Question

Solve the equation(The real numbers system)

x \in \emptyset

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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{2}{97} - \frac{44}{97} i, x_{2} = - \frac{2}{97} + \frac{44}{97} i

Alternative Form

x_{1} \approx - 0.020619 - 0.453608 i, x_{2} \approx - 0.020619 + 0.453608 i

Evaluate

(5 x + 6)^{2} + (13 x - 2)^{2} = 0

Expand the expression

More Steps

194 x^{2} + 8 x + 40 = 0

Substitute a= 194,b= 8 and c= 40 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 8 \pm 8 ^{2} - 4 \times 194 \times 40}{2 \times 194}

Simplify the expression

x = \frac{- 8 \pm 8 ^{2} - 4 \times 194 \times 40}{388}

Simplify the expression

More Steps

x = \frac{- 8 \pm - 30976}{388}

Simplify the radical expression

More Steps

x = \frac{- 8 \pm 176 i}{388}

Separate the equation into 2 possible cases

x = \frac{- 8 + 176 i}{388} x = \frac{- 8 - 176 i}{388}

Simplify the expression

More Steps

x = - \frac{2}{97} + \frac{44}{97} i x = \frac{- 8 - 176 i}{388}

Simplify the expression

More Steps

x = - \frac{2}{97} + \frac{44}{97} i x = - \frac{2}{97} - \frac{44}{97} i

Solution

x_{1} = - \frac{2}{97} - \frac{44}{97} i, x_{2} = - \frac{2}{97} + \frac{44}{97} i

Alternative Form

x_{1} \approx - 0.020619 - 0.453608 i, x_{2} \approx - 0.020619 + 0.453608 i

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