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Simplifying x2 + -117x = 2916 Reorder the terms: -117x + x2 = 2916 Solving -117x + x2 = 2916 Solving for variable 'x'. Reorder the terms: -2916 + -117x + x2 = 2916 + -2916 Combine like terms: 2916 + -2916 = 0 -2916 + -117x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2916' to each side of the equation. -2916 + -117x + 2916 + x2 = 0 + 2916 Reorder the terms: -2916 + 2916 + -117x + x2 = 0 + 2916 Combine like terms: -2916 + 2916 = 0 0 + -117x + x2 = 0 + 2916 -117x + x2 = 0 + 2916 Combine like terms: 0 + 2916 = 2916 -117x + x2 = 2916 The x term is -117x. Take half its coefficient (-58.5). Square it (3422.25) and add it to both sides. Add '3422.25' to each side of the equation. -117x + 3422.25 + x2 = 2916 + 3422.25 Reorder the terms: 3422.25 + -117x + x2 = 2916 + 3422.25 Combine like terms: 2916 + 3422.25 = 6338.25 3422.25 + -117x + x2 = 6338.25 Factor a perfect square on the left side: (x + -58.5)(x + -58.5) = 6338.25 Calculate the square root of the right side: 79.613127058 Break this problem into two subproblems by setting (x + -58.5) equal to 79.613127058 and -79.613127058.Subproblem 1
x + -58.5 = 79.613127058 Simplifying x + -58.5 = 79.613127058 Reorder the terms: -58.5 + x = 79.613127058 Solving -58.5 + x = 79.613127058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = 79.613127058 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = 79.613127058 + 58.5 x = 79.613127058 + 58.5 Combine like terms: 79.613127058 + 58.5 = 138.113127058 x = 138.113127058 Simplifying x = 138.113127058Subproblem 2
x + -58.5 = -79.613127058 Simplifying x + -58.5 = -79.613127058 Reorder the terms: -58.5 + x = -79.613127058 Solving -58.5 + x = -79.613127058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58.5' to each side of the equation. -58.5 + 58.5 + x = -79.613127058 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + x = -79.613127058 + 58.5 x = -79.613127058 + 58.5 Combine like terms: -79.613127058 + 58.5 = -21.113127058 x = -21.113127058 Simplifying x = -21.113127058Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.113127058, -21.113127058}
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