Solve √(3x + 5) = x. What is x?

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Multiple Choice

Solve √(3x + 5) = x. What is x?

Explanation:
The key idea is that the square root yields a nonnegative value, so x must be at least 0. Start by squaring both sides: (√(3x+5))^2 = x^2, giving 3x + 5 = x^2. Rearrange to a standard quadratic: x^2 - 3x - 5 = 0. Solve with the quadratic formula: x = [3 ± √(9 + 20)]/2 = [3 ± √29]/2. This gives two candidates: (3 + √29)/2 and (3 - √29)/2. The second candidate is negative (since √29 > 5), which cannot equal the nonnegative left side, so it doesn’t satisfy the original equation. The first candidate is positive and satisfies the equation after checking, so the solution is x = (3 + √29)/2.

The key idea is that the square root yields a nonnegative value, so x must be at least 0. Start by squaring both sides: (√(3x+5))^2 = x^2, giving 3x + 5 = x^2. Rearrange to a standard quadratic: x^2 - 3x - 5 = 0. Solve with the quadratic formula: x = [3 ± √(9 + 20)]/2 = [3 ± √29]/2. This gives two candidates: (3 + √29)/2 and (3 - √29)/2. The second candidate is negative (since √29 > 5), which cannot equal the nonnegative left side, so it doesn’t satisfy the original equation. The first candidate is positive and satisfies the equation after checking, so the solution is x = (3 + √29)/2.

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