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Simplifying x2 + -1950x + 15000 = 0 Reorder the terms: 15000 + -1950x + x2 = 0 Solving 15000 + -1950x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15000' to each side of the equation. 15000 + -1950x + -15000 + x2 = 0 + -15000 Reorder the terms: 15000 + -15000 + -1950x + x2 = 0 + -15000 Combine like terms: 15000 + -15000 = 0 0 + -1950x + x2 = 0 + -15000 -1950x + x2 = 0 + -15000 Combine like terms: 0 + -15000 = -15000 -1950x + x2 = -15000 The x term is -1950x. Take half its coefficient (-975). Square it (950625) and add it to both sides. Add '950625' to each side of the equation. -1950x + 950625 + x2 = -15000 + 950625 Reorder the terms: 950625 + -1950x + x2 = -15000 + 950625 Combine like terms: -15000 + 950625 = 935625 950625 + -1950x + x2 = 935625 Factor a perfect square on the left side: (x + -975)(x + -975) = 935625 Calculate the square root of the right side: 967.277106108 Break this problem into two subproblems by setting (x + -975) equal to 967.277106108 and -967.277106108.Subproblem 1
x + -975 = 967.277106108 Simplifying x + -975 = 967.277106108 Reorder the terms: -975 + x = 967.277106108 Solving -975 + x = 967.277106108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '975' to each side of the equation. -975 + 975 + x = 967.277106108 + 975 Combine like terms: -975 + 975 = 0 0 + x = 967.277106108 + 975 x = 967.277106108 + 975 Combine like terms: 967.277106108 + 975 = 1942.277106108 x = 1942.277106108 Simplifying x = 1942.277106108Subproblem 2
x + -975 = -967.277106108 Simplifying x + -975 = -967.277106108 Reorder the terms: -975 + x = -967.277106108 Solving -975 + x = -967.277106108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '975' to each side of the equation. -975 + 975 + x = -967.277106108 + 975 Combine like terms: -975 + 975 = 0 0 + x = -967.277106108 + 975 x = -967.277106108 + 975 Combine like terms: -967.277106108 + 975 = 7.722893892 x = 7.722893892 Simplifying x = 7.722893892Solution
The solution to the problem is based on the solutions from the subproblems. x = {1942.277106108, 7.722893892}
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