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Simplifying x(100 + -1x) + 1600 = 0 (100 * x + -1x * x) + 1600 = 0 (100x + -1x2) + 1600 = 0 Reorder the terms: 1600 + 100x + -1x2 = 0 Solving 1600 + 100x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1600 + -100x + x2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + -100x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -100x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -100x + x2 = 0 + 1600 -100x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -100x + x2 = 1600 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 = 1600 + 2500 Reorder the terms: 2500 + -100x + x2 = 1600 + 2500 Combine like terms: 1600 + 2500 = 4100 2500 + -100x + x2 = 4100 Factor a perfect square on the left side: (x + -50)(x + -50) = 4100 Calculate the square root of the right side: 64.031242374 Break this problem into two subproblems by setting (x + -50) equal to 64.031242374 and -64.031242374.Subproblem 1
x + -50 = 64.031242374 Simplifying x + -50 = 64.031242374 Reorder the terms: -50 + x = 64.031242374 Solving -50 + x = 64.031242374 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 = 64.031242374 + 50 Combine like terms: -50 + 50 = 0 0 + x = 64.031242374 + 50 x = 64.031242374 + 50 Combine like terms: 64.031242374 + 50 = 114.031242374 x = 114.031242374 Simplifying x = 114.031242374Subproblem 2
x + -50 = -64.031242374 Simplifying x + -50 = -64.031242374 Reorder the terms: -50 + x = -64.031242374 Solving -50 + x = -64.031242374 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 = -64.031242374 + 50 Combine like terms: -50 + 50 = 0 0 + x = -64.031242374 + 50 x = -64.031242374 + 50 Combine like terms: -64.031242374 + 50 = -14.031242374 x = -14.031242374 Simplifying x = -14.031242374Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.031242374, -14.031242374}
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