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Simplifying x2 + -100x + -2475 = 0 Reorder the terms: -2475 + -100x + x2 = 0 Solving -2475 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2475' to each side of the equation. -2475 + -100x + 2475 + x2 = 0 + 2475 Reorder the terms: -2475 + 2475 + -100x + x2 = 0 + 2475 Combine like terms: -2475 + 2475 = 0 0 + -100x + x2 = 0 + 2475 -100x + x2 = 0 + 2475 Combine like terms: 0 + 2475 = 2475 -100x + x2 = 2475 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 = 2475 + 2500 Reorder the terms: 2500 + -100x + x2 = 2475 + 2500 Combine like terms: 2475 + 2500 = 4975 2500 + -100x + x2 = 4975 Factor a perfect square on the left side: (x + -50)(x + -50) = 4975 Calculate the square root of the right side: 70.533679898 Break this problem into two subproblems by setting (x + -50) equal to 70.533679898 and -70.533679898.Subproblem 1
x + -50 = 70.533679898 Simplifying x + -50 = 70.533679898 Reorder the terms: -50 + x = 70.533679898 Solving -50 + x = 70.533679898 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 = 70.533679898 + 50 Combine like terms: -50 + 50 = 0 0 + x = 70.533679898 + 50 x = 70.533679898 + 50 Combine like terms: 70.533679898 + 50 = 120.533679898 x = 120.533679898 Simplifying x = 120.533679898Subproblem 2
x + -50 = -70.533679898 Simplifying x + -50 = -70.533679898 Reorder the terms: -50 + x = -70.533679898 Solving -50 + x = -70.533679898 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 = -70.533679898 + 50 Combine like terms: -50 + 50 = 0 0 + x = -70.533679898 + 50 x = -70.533679898 + 50 Combine like terms: -70.533679898 + 50 = -20.533679898 x = -20.533679898 Simplifying x = -20.533679898Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.533679898, -20.533679898}
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