Solve x^2 90=22x-31

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{11}{90} - \frac{2669}{90} i, x_{2} = \frac{11}{90} + \frac{2669}{90} i

Alternative Form

x_{1} \approx 0.1 \dot{2} - 0.574026 i, x_{2} \approx 0.1 \dot{2} + 0.574026 i

Evaluate

x^{2} \times 90 = 22 x - 31

Use the commutative property to reorder the terms

90 x^{2} = 22 x - 31

Move the expression to the left side

90 x^{2} - 22 x + 31 = 0

Substitute a= 90,b= - 22 and c= 31 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{22 \pm ( - 22 ) ^{2} - 4 \times 90 \times 31}{2 \times 90}

Simplify the expression

x = \frac{22 \pm ( - 22 ) ^{2} - 4 \times 90 \times 31}{180}

Simplify the expression

More Steps

x = \frac{22 \pm - 10676}{180}

Simplify the radical expression

More Steps

x = \frac{22 \pm 2 2669 \times i}{180}

Separate the equation into 2 possible cases

x = \frac{22 + 2 2669 \times i}{180} x = \frac{22 - 2 2669 \times i}{180}

Simplify the expression

More Steps

x = \frac{11}{90} + \frac{2669}{90} i x = \frac{22 - 2 2669 \times i}{180}

Simplify the expression

More Steps

x = \frac{11}{90} + \frac{2669}{90} i x = \frac{11}{90} - \frac{2669}{90} i

Solution

x_{1} = \frac{11}{90} - \frac{2669}{90} i, x_{2} = \frac{11}{90} + \frac{2669}{90} i

Alternative Form

x_{1} \approx 0.1 \dot{2} - 0.574026 i, x_{2} \approx 0.1 \dot{2} + 0.574026 i

Show Solution