Resolved: "What is x if 3x−2(x−3)2=2x+7−5x?"

tlhalakq9

Answered question

2022-02-05

What is x if

3 x - \sqrt{2 {(x - 3)}^{2}} = 2 x + 7 - 5 x

narodiloxe4

Beginner2022-02-06Added 19 answers

Step 1

3 x - \sqrt{2 \cdot {(x - 3)}^{2}} = 2 x + 7 - 5 x

3 x - \sqrt{2 \cdot {(x - 3)}^{2}} = 7 - 3 x

3 x + 3 x - 7 = \sqrt{2 \cdot {(x - 3)}^{2}}

6 x - 7 = \sqrt{2 \cdot {(x - 3)}^{2}}

{(6 x - 7)}^{2} = 2 \cdot {(x - 3)}^{2}

36 x^{2} - 84 x + 49 = 2 \cdot (x^{2} - 6 x + 9)

36 x^{2} - 84 x + 49 = 2 x^{2} - 12 x + 18

34 x^{2} - 72 x + 31 = 0

Δ = {(- 72)}^{2} - 4 \cdot 34 \cdot 31 = 968 = {(22 \sqrt{2})}^{2}

Hence

x_{1} = \frac{72 + 22 \sqrt{2}}{34 \cdot 2} = \frac{36 + 11 \sqrt{2}}{34} and x_{2} = \frac{72 - 22 \sqrt{2}}{34 \cdot 2} = \frac{36 - 11 \sqrt{2}}{34}

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