Question

Solve √(37 - x^2) + 5 = x.

Answer 1

To solve √(37 - x^2) + 5 = x, follow these steps: subtract 5, square both sides, simplify, rearrange, factor, and solve for x. The solutions are x = 6 and x = -1.

Step-by-step explanation:

To solve the equation √(37 - x^2) + 5 = x, we need to isolate the square root term and then square both sides of the equation to eliminate the square root. Here are the steps:

1. Subtract 5 from both sides: √(37 - x^2) = x - 5
2. Square both sides of the equation: (√(37 - x^2))^2 = (x - 5)^2
3. Simplify: 37 - x^2 = (x - 5)^2
4. Expand the right side: 37 - x^2 = x^2 - 10x + 25
5. Rearrange the equation: 2x^2 - 10x - 12 = 0
6. Factor: 2(x - 6)(x + 1) = 0
7. Set each factor equal to zero and solve for x: x - 6 = 0 or x + 1 = 0
8. Solve for x: x = 6 or x = -1

Therefore, the solutions to the equation are x = 6 and x = -1.

Learn more about Solving square root equations