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Simplifying x(x + 100) = 110 Reorder the terms: x(100 + x) = 110 (100 * x + x * x) = 110 (100x + x2) = 110 Solving 100x + x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 100x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 100x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 100x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 100x + x2 = 0 + 110 100x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 100x + x2 = 110 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 = 110 + 2500 Reorder the terms: 2500 + 100x + x2 = 110 + 2500 Combine like terms: 110 + 2500 = 2610 2500 + 100x + x2 = 2610 Factor a perfect square on the left side: (x + 50)(x + 50) = 2610 Calculate the square root of the right side: 51.088159098 Break this problem into two subproblems by setting (x + 50) equal to 51.088159098 and -51.088159098.Subproblem 1
x + 50 = 51.088159098 Simplifying x + 50 = 51.088159098 Reorder the terms: 50 + x = 51.088159098 Solving 50 + x = 51.088159098 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 = 51.088159098 + -50 Combine like terms: 50 + -50 = 0 0 + x = 51.088159098 + -50 x = 51.088159098 + -50 Combine like terms: 51.088159098 + -50 = 1.088159098 x = 1.088159098 Simplifying x = 1.088159098Subproblem 2
x + 50 = -51.088159098 Simplifying x + 50 = -51.088159098 Reorder the terms: 50 + x = -51.088159098 Solving 50 + x = -51.088159098 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 = -51.088159098 + -50 Combine like terms: 50 + -50 = 0 0 + x = -51.088159098 + -50 x = -51.088159098 + -50 Combine like terms: -51.088159098 + -50 = -101.088159098 x = -101.088159098 Simplifying x = -101.088159098Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.088159098, -101.088159098}
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