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Simplifying (1000 + 1000x) * x + 1000 = 1041.34 Reorder the terms for easier multiplication: x(1000 + 1000x) + 1000 = 1041.34 (1000 * x + 1000x * x) + 1000 = 1041.34 (1000x + 1000x2) + 1000 = 1041.34 Reorder the terms: 1000 + 1000x + 1000x2 = 1041.34 Solving 1000 + 1000x + 1000x2 = 1041.34 Solving for variable 'x'. Reorder the terms: 1000 + -1041.34 + 1000x + 1000x2 = 1041.34 + -1041.34 Combine like terms: 1000 + -1041.34 = -41.34 -41.34 + 1000x + 1000x2 = 1041.34 + -1041.34 Combine like terms: 1041.34 + -1041.34 = 0.00 -41.34 + 1000x + 1000x2 = 0.00 Begin completing the square. Divide all terms by 1000 the coefficient of the squared term: Divide each side by '1000'. -0.04134 + x + x2 = 0.00 Move the constant term to the right: Add '0.04134' to each side of the equation. -0.04134 + x + 0.04134 + x2 = 0.00 + 0.04134 Reorder the terms: -0.04134 + 0.04134 + x + x2 = 0.00 + 0.04134 Combine like terms: -0.04134 + 0.04134 = 0.00000 0.00000 + x + x2 = 0.00 + 0.04134 x + x2 = 0.00 + 0.04134 Combine like terms: 0.00 + 0.04134 = 0.04134 x + x2 = 0.04134 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.04134 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.04134 + 0.25 Combine like terms: 0.04134 + 0.25 = 0.29134 1.25 + x2 = 0.29134 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.29134 Calculate the square root of the right side: 0.539759206 Break this problem into two subproblems by setting (x + 0.5) equal to 0.539759206 and -0.539759206.Subproblem 1
x + 0.5 = 0.539759206 Simplifying x + 0.5 = 0.539759206 Reorder the terms: 0.5 + x = 0.539759206 Solving 0.5 + x = 0.539759206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.539759206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.539759206 + -0.5 x = 0.539759206 + -0.5 Combine like terms: 0.539759206 + -0.5 = 0.039759206 x = 0.039759206 Simplifying x = 0.039759206Subproblem 2
x + 0.5 = -0.539759206 Simplifying x + 0.5 = -0.539759206 Reorder the terms: 0.5 + x = -0.539759206 Solving 0.5 + x = -0.539759206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.539759206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.539759206 + -0.5 x = -0.539759206 + -0.5 Combine like terms: -0.539759206 + -0.5 = -1.039759206 x = -1.039759206 Simplifying x = -1.039759206Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039759206, -1.039759206}
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