What is the answer to |x-5|^2+|x-5|-24=0 ?

The answer to |x-5|^2+|x-5|-24=0 is x=(11-sqrt(97))/2 \lor x=(9+sqrt(97))/2

Solve for x: |x-5|^2+|x-5|-24=0

The solution is x=(11-sqrt(97))/2 \lor x=(9+sqrt(97))/2

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∣ x - 5 ∣^{2} + ∣ x - 5 ∣ - 24 = 0

x = \frac{11 - 97}{2} or x = \frac{9 + 97}{2}

Solution steps

∣ x - 5 ∣^{2} + ∣ x - 5 ∣ - 24 = 0

Find positive and negative intervals

x < 5, x \geq 5

Solve the inequality for each interval

x = \frac{11 - 97}{2} or x = \frac{9 + 97}{2}

1 x^{2} - x + ∣ x + 1 ∣ = 5

∣ 3 x + 2 ∣ = x + 1, ∣ 2 x - 3 ∣ = x - 5, ∣ 3 x - 2 ∣ = 2 x + 3

y, 17 x^{2} - 16 ∣ x ∣ y + 17 y^{2} = 225

x^{2} + 2 ∣ x ∣ = 15

x^{2} + x + 4 = 0

What is the answer to |x-5|^2+|x-5|-24=0 ?
The answer to |x-5|^2+|x-5|-24=0 is x=(11-sqrt(97))/2 \lor x=(9+sqrt(97))/2
Solve for x: |x-5|^2+|x-5|-24=0
The solution is x=(11-sqrt(97))/2 \lor x=(9+sqrt(97))/2