Solve x^4= (x-20)^2

Question

Solve the equation

x_{1} = - 5, x_{2} = 4

Evaluate

x^{4} = (x - 20)^{2}

Raise both sides of the equation to the reciprocal of the exponent

(x^{4})^{\frac{1}{2}} = ((x - 20)^{2})^{\frac{1}{2}}

Evaluate the power

x^{2} = ∣ x - 20 ∣

Swap the sides

∣ x - 20 ∣ = x^{2}

Rewrite the expression

∣ x - 20 ∣ - x^{2} = 0

Separate the equation into 2 possible cases

x - 20 - x^{2} = 0, x - 20 \geq 0 - (x - 20) - x^{2} = 0, x - 20 < 0

Solve the equation

More Steps

x \in / R, x - 20 \geq 0 - (x - 20) - x^{2} = 0, x - 20 < 0

Solve the inequality

More Steps

x \in / R, x \geq 20 - (x - 20) - x^{2} = 0, x - 20 < 0

Solve the equation

More Steps

x \in / R, x \geq 20 x = 4 x = - 5, x - 20 < 0

Solve the inequality

More Steps

x \in / R, x \geq 20 x = 4 x = - 5, x < 20

Find the intersection

x \in / R x = 4 x = - 5, x < 20

Find the intersection

x \in / R x = 4 x = - 5

Find the union

x = 4 x = - 5

Solution

x_{1} = - 5, x_{2} = 4

Show Solution