Solve (x^2)2=(x-4)2

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}{2} - \frac{15}{2} i, x_{2} = \frac{1}{2} + \frac{15}{2} i

Alternative Form

x_{1} \approx 0.5 - 1.936492 i, x_{2} \approx 0.5 + 1.936492 i

Evaluate

x^{2} \times 2 = (x - 4) \times 2

Use the commutative property to reorder the terms

2 x^{2} = (x - 4) \times 2

Multiply the terms

2 x^{2} = 2 (x - 4)

Expand the expression

More Steps

2 x^{2} = 2 x - 8

Move the expression to the left side

2 x^{2} - 2 x + 8 = 0

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

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 \times 8}{2 \times 2}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 \times 8}{4}

Simplify the expression

More Steps

x = \frac{2 \pm - 60}{4}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 15 \times i}{4}

Separate the equation into 2 possible cases

x = \frac{2 + 2 15 \times i}{4} x = \frac{2 - 2 15 \times i}{4}

Simplify the expression

More Steps

x = \frac{1}{2} + \frac{15}{2} i x = \frac{2 - 2 15 \times i}{4}

Simplify the expression

More Steps

x = \frac{1}{2} + \frac{15}{2} i x = \frac{1}{2} - \frac{15}{2} i

Solution

x_{1} = \frac{1}{2} - \frac{15}{2} i, x_{2} = \frac{1}{2} + \frac{15}{2} i

Alternative Form

x_{1} \approx 0.5 - 1.936492 i, x_{2} \approx 0.5 + 1.936492 i

Show Solution