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Simplifying 0 = -1x2 + 100x + 1000 Reorder the terms: 0 = 1000 + 100x + -1x2 Solving 0 = 1000 + 100x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + -100x + x2 = 1000 + 100x + -1x2 + -1000 + -100x + x2 Reorder the terms: -1000 + -100x + x2 = 1000 + -1000 + 100x + -100x + -1x2 + x2 Combine like terms: 1000 + -1000 = 0 -1000 + -100x + x2 = 0 + 100x + -100x + -1x2 + x2 -1000 + -100x + x2 = 100x + -100x + -1x2 + x2 Combine like terms: 100x + -100x = 0 -1000 + -100x + x2 = 0 + -1x2 + x2 -1000 + -100x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1000 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -100x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -100x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -100x + x2 = 0 + 1000 -100x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -100x + x2 = 1000 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 = 1000 + 2500 Reorder the terms: 2500 + -100x + x2 = 1000 + 2500 Combine like terms: 1000 + 2500 = 3500 2500 + -100x + x2 = 3500 Factor a perfect square on the left side: (x + -50)(x + -50) = 3500 Calculate the square root of the right side: 59.160797831 Break this problem into two subproblems by setting (x + -50) equal to 59.160797831 and -59.160797831.Subproblem 1
x + -50 = 59.160797831 Simplifying x + -50 = 59.160797831 Reorder the terms: -50 + x = 59.160797831 Solving -50 + x = 59.160797831 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 = 59.160797831 + 50 Combine like terms: -50 + 50 = 0 0 + x = 59.160797831 + 50 x = 59.160797831 + 50 Combine like terms: 59.160797831 + 50 = 109.160797831 x = 109.160797831 Simplifying x = 109.160797831Subproblem 2
x + -50 = -59.160797831 Simplifying x + -50 = -59.160797831 Reorder the terms: -50 + x = -59.160797831 Solving -50 + x = -59.160797831 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 = -59.160797831 + 50 Combine like terms: -50 + 50 = 0 0 + x = -59.160797831 + 50 x = -59.160797831 + 50 Combine like terms: -59.160797831 + 50 = -9.160797831 x = -9.160797831 Simplifying x = -9.160797831Solution
The solution to the problem is based on the solutions from the subproblems. x = {109.160797831, -9.160797831}
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