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Simplifying 45x + x2 = 500 Solving 45x + x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 45x + x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 45x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 45x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 45x + x2 = 0 + 500 45x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 45x + x2 = 500 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 500 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 500 + 506.25 Combine like terms: 500 + 506.25 = 1006.25 506.25 + 45x + x2 = 1006.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 1006.25 Calculate the square root of the right side: 31.721443851 Break this problem into two subproblems by setting (x + 22.5) equal to 31.721443851 and -31.721443851.Subproblem 1
x + 22.5 = 31.721443851 Simplifying x + 22.5 = 31.721443851 Reorder the terms: 22.5 + x = 31.721443851 Solving 22.5 + x = 31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 31.721443851 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 31.721443851 + -22.5 x = 31.721443851 + -22.5 Combine like terms: 31.721443851 + -22.5 = 9.221443851 x = 9.221443851 Simplifying x = 9.221443851Subproblem 2
x + 22.5 = -31.721443851 Simplifying x + 22.5 = -31.721443851 Reorder the terms: 22.5 + x = -31.721443851 Solving 22.5 + x = -31.721443851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -31.721443851 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -31.721443851 + -22.5 x = -31.721443851 + -22.5 Combine like terms: -31.721443851 + -22.5 = -54.221443851 x = -54.221443851 Simplifying x = -54.221443851Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.221443851, -54.221443851}
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