Solve 2x^29=6x-9 - ScanMath

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}{6} - \frac{17}{6} i, x_{2} = \frac{1}{6} + \frac{17}{6} i

Alternative Form

x_{1} \approx 0.1 \dot{6} - 0.687184 i, x_{2} \approx 0.1 \dot{6} + 0.687184 i

Evaluate

2 x^{2} \times 9 = 6 x - 9

Multiply the terms

18 x^{2} = 6 x - 9

Move the expression to the left side

18 x^{2} - 6 x + 9 = 0

Substitute a= 18,b= - 6 and c= 9 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 18 \times 9}{2 \times 18}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 18 \times 9}{36}

Simplify the expression

More Steps

x = \frac{6 \pm - 612}{36}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 17 \times i}{36}

Separate the equation into 2 possible cases

x = \frac{6 + 6 17 \times i}{36} x = \frac{6 - 6 17 \times i}{36}

Simplify the expression

More Steps

x = \frac{1}{6} + \frac{17}{6} i x = \frac{6 - 6 17 \times i}{36}

Simplify the expression

More Steps

x = \frac{1}{6} + \frac{17}{6} i x = \frac{1}{6} - \frac{17}{6} i

Solution

x_{1} = \frac{1}{6} - \frac{17}{6} i, x_{2} = \frac{1}{6} + \frac{17}{6} i

Alternative Form

x_{1} \approx 0.1 \dot{6} - 0.687184 i, x_{2} \approx 0.1 \dot{6} + 0.687184 i

Show Solution