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Simplifying 1360 = 0.07x(19000 + -1x) * 0.08 Reorder the terms for easier multiplication: 1360 = 0.07 * 0.08x(19000 + -1x) Multiply 0.07 * 0.08 1360 = 0.0056x(19000 + -1x) 1360 = (19000 * 0.0056x + -1x * 0.0056x) 1360 = (106.4x + -0.0056x2) Solving 1360 = 106.4x + -0.0056x2 Solving for variable 'x'. Reorder the terms: 1360 + -106.4x + 0.0056x2 = 106.4x + -106.4x + -0.0056x2 + 0.0056x2 Combine like terms: 106.4x + -106.4x = 0.0 1360 + -106.4x + 0.0056x2 = 0.0 + -0.0056x2 + 0.0056x2 1360 + -106.4x + 0.0056x2 = -0.0056x2 + 0.0056x2 Combine like terms: -0.0056x2 + 0.0056x2 = 0.0000 1360 + -106.4x + 0.0056x2 = 0.0000 Begin completing the square. Divide all terms by 0.0056 the coefficient of the squared term: Divide each side by '0.0056'. 242857.1429 + -19000x + x2 = 0 Move the constant term to the right: Add '-242857.1429' to each side of the equation. 242857.1429 + -19000x + -242857.1429 + x2 = 0 + -242857.1429 Reorder the terms: 242857.1429 + -242857.1429 + -19000x + x2 = 0 + -242857.1429 Combine like terms: 242857.1429 + -242857.1429 = 0.0000 0.0000 + -19000x + x2 = 0 + -242857.1429 -19000x + x2 = 0 + -242857.1429 Combine like terms: 0 + -242857.1429 = -242857.1429 -19000x + x2 = -242857.1429 The x term is -19000x. Take half its coefficient (-9500). Square it (90250000) and add it to both sides. Add '90250000' to each side of the equation. -19000x + 90250000 + x2 = -242857.1429 + 90250000 Reorder the terms: 90250000 + -19000x + x2 = -242857.1429 + 90250000 Combine like terms: -242857.1429 + 90250000 = 90007142.8571 90250000 + -19000x + x2 = 90007142.8571 Factor a perfect square on the left side: (x + -9500)(x + -9500) = 90007142.8571 Calculate the square root of the right side: 9487.20943466 Break this problem into two subproblems by setting (x + -9500) equal to 9487.20943466 and -9487.20943466.Subproblem 1
x + -9500 = 9487.20943466 Simplifying x + -9500 = 9487.20943466 Reorder the terms: -9500 + x = 9487.20943466 Solving -9500 + x = 9487.20943466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9500' to each side of the equation. -9500 + 9500 + x = 9487.20943466 + 9500 Combine like terms: -9500 + 9500 = 0 0 + x = 9487.20943466 + 9500 x = 9487.20943466 + 9500 Combine like terms: 9487.20943466 + 9500 = 18987.20943466 x = 18987.20943466 Simplifying x = 18987.20943466Subproblem 2
x + -9500 = -9487.20943466 Simplifying x + -9500 = -9487.20943466 Reorder the terms: -9500 + x = -9487.20943466 Solving -9500 + x = -9487.20943466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9500' to each side of the equation. -9500 + 9500 + x = -9487.20943466 + 9500 Combine like terms: -9500 + 9500 = 0 0 + x = -9487.20943466 + 9500 x = -9487.20943466 + 9500 Combine like terms: -9487.20943466 + 9500 = 12.79056534 x = 12.79056534 Simplifying x = 12.79056534Solution
The solution to the problem is based on the solutions from the subproblems. x = {18987.20943466, 12.79056534}
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