What is the answer to (x-3)^2+|x-3|-11=0 ?

The answer to (x-3)^2+|x-3|-11=0 is x=(7-3sqrt(5))/2 \lor x=(5+3sqrt(5))/2

Solve for x: (x-3)^2+|x-3|-11=0

The solution is x=(7-3sqrt(5))/2 \lor x=(5+3sqrt(5))/2

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(x - 3)^{2} + ∣ x - 3 ∣ - 11 = 0

x = \frac{7 - 3 5}{2} or x = \frac{5 + 3 5}{2}

Decimal Notation

x = 0.14589 \dots, x = 5.85410 \dots

Solution steps

(x - 3)^{2} + ∣ x - 3 ∣ - 11 = 0

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

x = \frac{7 - 3 5}{2} or x = \frac{5 + 3 5}{2}

x^{2} - 3 x + 2 - x^{2} - 5 x + 4 = 2 x^{2} - 8 x + 6

∣ 3 x - 1 ∣ = 4

∣ x ∣ + x = 0

∣ x - 1 ∣ = 4 - x

∣ x - 1 ∣ = ∣ x + 4 ∣

What is the answer to (x-3)^2+|x-3|-11=0 ?
The answer to (x-3)^2+|x-3|-11=0 is x=(7-3sqrt(5))/2 \lor x=(5+3sqrt(5))/2
Solve for x: (x-3)^2+|x-3|-11=0
The solution is x=(7-3sqrt(5))/2 \lor x=(5+3sqrt(5))/2