Solve |x^2| |x-5| =|x| - ScanMath

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Type your math problem... |x^2| |x-5| =|x|

Question

Solve the equation

x_{1} = \frac{5 - 29}{2}, x_{2} = 0, x_{3} = \frac{5 - 21}{2}, x_{4} = \frac{5 + 21}{2}, x_{5} = \frac{5 + 29}{2}

Alternative Form

x_{1} \approx - 0.192582, x_{2} = 0, x_{3} \approx 0.208712, x_{4} \approx 4.791288, x_{5} \approx 5.192582

Evaluate

x^{2} ∣ x - 5 ∣ = ∣ x ∣

When the expression in absolute value bars is not negative, remove the bars

x^{2} ∣ x - 5 ∣ = ∣ x ∣

Swap the sides

∣ x ∣ = x^{2} ∣ x - 5 ∣

Move the expression to the left side

∣ x ∣ - x^{2} ∣ x - 5 ∣ = 0

Separate the equation into 4 possible cases

x - x^{2} (x - 5) = 0, x \geq 0, x - 5 \geq 0 x - x^{2} (- (x - 5)) = 0, x \geq 0, x - 5 < 0 - x - x^{2} (x - 5) = 0, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the equation

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x - 5 \geq 0 x - x^{2} (- (x - 5)) = 0, x \geq 0, x - 5 < 0 - x - x^{2} (x - 5) = 0, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the inequality

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x - x^{2} (- (x - 5)) = 0, x \geq 0, x - 5 < 0 - x - x^{2} (x - 5) = 0, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the equation

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x - 5 < 0 - x - x^{2} (x - 5) = 0, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the inequality

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 - x - x^{2} (x - 5) = 0, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the equation

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x - 5 \geq 0 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the inequality

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x \geq 5 - x - x^{2} (- (x - 5)) = 0, x < 0, x - 5 < 0

Solve the equation

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x \geq 5 x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x < 0, x - 5 < 0

Solve the inequality

More Steps

x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x \geq 0, x \geq 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x \geq 5 x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x < 0, x < 5

Find the intersection

x = \frac{5 + 29}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x \geq 0, x < 5 x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x \geq 5 x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x < 0, x < 5

Find the intersection

x = \frac{5 + 29}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2}, x < 0, x \geq 5 x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x < 0, x < 5

Find the intersection

x = \frac{5 + 29}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2} x \in \emptyset x = 0 x = \frac{5 + 29}{2} x = \frac{5 - 29}{2}, x < 0, x < 5

Find the intersection

x = \frac{5 + 29}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2} x \in \emptyset x = \frac{5 - 29}{2}

Find the union

x = \frac{5 + 29}{2} x = 0 x = \frac{5 + 21}{2} x = \frac{5 - 21}{2} x = \frac{5 - 29}{2}

Solution

x_{1} = \frac{5 - 29}{2}, x_{2} = 0, x_{3} = \frac{5 - 21}{2}, x_{4} = \frac{5 + 21}{2}, x_{5} = \frac{5 + 29}{2}

Alternative Form

x_{1} \approx - 0.192582, x_{2} = 0, x_{3} \approx 0.208712, x_{4} \approx 4.791288, x_{5} \approx 5.192582

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