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Simplifying x(x + 45) = 117 Reorder the terms: x(45 + x) = 117 (45 * x + x * x) = 117 (45x + x2) = 117 Solving 45x + x2 = 117 Solving for variable 'x'. Reorder the terms: -117 + 45x + x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -117 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 45x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + 45x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 45x + x2 = 0 + 117 45x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 45x + x2 = 117 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 = 117 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 117 + 506.25 Combine like terms: 117 + 506.25 = 623.25 506.25 + 45x + x2 = 623.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 623.25 Calculate the square root of the right side: 24.964975466 Break this problem into two subproblems by setting (x + 22.5) equal to 24.964975466 and -24.964975466.Subproblem 1
x + 22.5 = 24.964975466 Simplifying x + 22.5 = 24.964975466 Reorder the terms: 22.5 + x = 24.964975466 Solving 22.5 + x = 24.964975466 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 = 24.964975466 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 24.964975466 + -22.5 x = 24.964975466 + -22.5 Combine like terms: 24.964975466 + -22.5 = 2.464975466 x = 2.464975466 Simplifying x = 2.464975466Subproblem 2
x + 22.5 = -24.964975466 Simplifying x + 22.5 = -24.964975466 Reorder the terms: 22.5 + x = -24.964975466 Solving 22.5 + x = -24.964975466 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 = -24.964975466 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -24.964975466 + -22.5 x = -24.964975466 + -22.5 Combine like terms: -24.964975466 + -22.5 = -47.464975466 x = -47.464975466 Simplifying x = -47.464975466Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.464975466, -47.464975466}
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