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Simplifying x2 + -100x + 240 = 0 Reorder the terms: 240 + -100x + x2 = 0 Solving 240 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-240' to each side of the equation. 240 + -100x + -240 + x2 = 0 + -240 Reorder the terms: 240 + -240 + -100x + x2 = 0 + -240 Combine like terms: 240 + -240 = 0 0 + -100x + x2 = 0 + -240 -100x + x2 = 0 + -240 Combine like terms: 0 + -240 = -240 -100x + x2 = -240 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -240 + 2500 Reorder the terms: 2500 + -100x + x2 = -240 + 2500 Combine like terms: -240 + 2500 = 2260 2500 + -100x + x2 = 2260 Factor a perfect square on the left side: (x + -50)(x + -50) = 2260 Calculate the square root of the right side: 47.539457296 Break this problem into two subproblems by setting (x + -50) equal to 47.539457296 and -47.539457296.Subproblem 1
x + -50 = 47.539457296 Simplifying x + -50 = 47.539457296 Reorder the terms: -50 + x = 47.539457296 Solving -50 + x = 47.539457296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 47.539457296 + 50 Combine like terms: -50 + 50 = 0 0 + x = 47.539457296 + 50 x = 47.539457296 + 50 Combine like terms: 47.539457296 + 50 = 97.539457296 x = 97.539457296 Simplifying x = 97.539457296Subproblem 2
x + -50 = -47.539457296 Simplifying x + -50 = -47.539457296 Reorder the terms: -50 + x = -47.539457296 Solving -50 + x = -47.539457296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -47.539457296 + 50 Combine like terms: -50 + 50 = 0 0 + x = -47.539457296 + 50 x = -47.539457296 + 50 Combine like terms: -47.539457296 + 50 = 2.460542704 x = 2.460542704 Simplifying x = 2.460542704Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.539457296, 2.460542704}
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