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Simplifying 1177 = 0.07x * x + 47.4x + 500 Multiply x * x 1177 = 0.07x2 + 47.4x + 500 Reorder the terms: 1177 = 500 + 47.4x + 0.07x2 Solving 1177 = 500 + 47.4x + 0.07x2 Solving for variable 'x'. Combine like terms: 1177 + -500 = 677 677 + -47.4x + -0.07x2 = 500 + 47.4x + 0.07x2 + -500 + -47.4x + -0.07x2 Reorder the terms: 677 + -47.4x + -0.07x2 = 500 + -500 + 47.4x + -47.4x + 0.07x2 + -0.07x2 Combine like terms: 500 + -500 = 0 677 + -47.4x + -0.07x2 = 0 + 47.4x + -47.4x + 0.07x2 + -0.07x2 677 + -47.4x + -0.07x2 = 47.4x + -47.4x + 0.07x2 + -0.07x2 Combine like terms: 47.4x + -47.4x = 0.0 677 + -47.4x + -0.07x2 = 0.0 + 0.07x2 + -0.07x2 677 + -47.4x + -0.07x2 = 0.07x2 + -0.07x2 Combine like terms: 0.07x2 + -0.07x2 = 0.00 677 + -47.4x + -0.07x2 = 0.00 Begin completing the square. Divide all terms by -0.07 the coefficient of the squared term: Divide each side by '-0.07'. -9671.428571 + 677.1428571x + x2 = 0 Move the constant term to the right: Add '9671.428571' to each side of the equation. -9671.428571 + 677.1428571x + 9671.428571 + x2 = 0 + 9671.428571 Reorder the terms: -9671.428571 + 9671.428571 + 677.1428571x + x2 = 0 + 9671.428571 Combine like terms: -9671.428571 + 9671.428571 = 0.000000 0.000000 + 677.1428571x + x2 = 0 + 9671.428571 677.1428571x + x2 = 0 + 9671.428571 Combine like terms: 0 + 9671.428571 = 9671.428571 677.1428571x + x2 = 9671.428571 The x term is 677.1428571x. Take half its coefficient (338.5714286). Square it (114630.6123) and add it to both sides. Add '114630.6123' to each side of the equation. 677.1428571x + 114630.6123 + x2 = 9671.428571 + 114630.6123 Reorder the terms: 114630.6123 + 677.1428571x + x2 = 9671.428571 + 114630.6123 Combine like terms: 9671.428571 + 114630.6123 = 124302.040871 114630.6123 + 677.1428571x + x2 = 124302.040871 Factor a perfect square on the left side: (x + 338.5714286)(x + 338.5714286) = 124302.040871 Calculate the square root of the right side: 352.564945607 Break this problem into two subproblems by setting (x + 338.5714286) equal to 352.564945607 and -352.564945607.Subproblem 1
x + 338.5714286 = 352.564945607 Simplifying x + 338.5714286 = 352.564945607 Reorder the terms: 338.5714286 + x = 352.564945607 Solving 338.5714286 + x = 352.564945607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-338.5714286' to each side of the equation. 338.5714286 + -338.5714286 + x = 352.564945607 + -338.5714286 Combine like terms: 338.5714286 + -338.5714286 = 0.0000000 0.0000000 + x = 352.564945607 + -338.5714286 x = 352.564945607 + -338.5714286 Combine like terms: 352.564945607 + -338.5714286 = 13.993517007 x = 13.993517007 Simplifying x = 13.993517007Subproblem 2
x + 338.5714286 = -352.564945607 Simplifying x + 338.5714286 = -352.564945607 Reorder the terms: 338.5714286 + x = -352.564945607 Solving 338.5714286 + x = -352.564945607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-338.5714286' to each side of the equation. 338.5714286 + -338.5714286 + x = -352.564945607 + -338.5714286 Combine like terms: 338.5714286 + -338.5714286 = 0.0000000 0.0000000 + x = -352.564945607 + -338.5714286 x = -352.564945607 + -338.5714286 Combine like terms: -352.564945607 + -338.5714286 = -691.136374207 x = -691.136374207 Simplifying x = -691.136374207Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.993517007, -691.136374207}
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