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Simplifying 6664 = -0.35x2 + 38.45x + 5819.90 Reorder the terms: 6664 = 5819.90 + 38.45x + -0.35x2 Solving 6664 = 5819.90 + 38.45x + -0.35x2 Solving for variable 'x'. Combine like terms: 6664 + -5819.90 = 844.1 844.1 + -38.45x + 0.35x2 = 5819.90 + 38.45x + -0.35x2 + -5819.90 + -38.45x + 0.35x2 Reorder the terms: 844.1 + -38.45x + 0.35x2 = 5819.90 + -5819.90 + 38.45x + -38.45x + -0.35x2 + 0.35x2 Combine like terms: 5819.90 + -5819.90 = 0.00 844.1 + -38.45x + 0.35x2 = 0.00 + 38.45x + -38.45x + -0.35x2 + 0.35x2 844.1 + -38.45x + 0.35x2 = 38.45x + -38.45x + -0.35x2 + 0.35x2 Combine like terms: 38.45x + -38.45x = 0.00 844.1 + -38.45x + 0.35x2 = 0.00 + -0.35x2 + 0.35x2 844.1 + -38.45x + 0.35x2 = -0.35x2 + 0.35x2 Combine like terms: -0.35x2 + 0.35x2 = 0.00 844.1 + -38.45x + 0.35x2 = 0.00 Begin completing the square. Divide all terms by 0.35 the coefficient of the squared term: Divide each side by '0.35'. 2411.714286 + -109.8571429x + x2 = 0 Move the constant term to the right: Add '-2411.714286' to each side of the equation. 2411.714286 + -109.8571429x + -2411.714286 + x2 = 0 + -2411.714286 Reorder the terms: 2411.714286 + -2411.714286 + -109.8571429x + x2 = 0 + -2411.714286 Combine like terms: 2411.714286 + -2411.714286 = 0.000000 0.000000 + -109.8571429x + x2 = 0 + -2411.714286 -109.8571429x + x2 = 0 + -2411.714286 Combine like terms: 0 + -2411.714286 = -2411.714286 -109.8571429x + x2 = -2411.714286 The x term is -109.8571429x. Take half its coefficient (-54.92857145). Square it (3017.147962) and add it to both sides. Add '3017.147962' to each side of the equation. -109.8571429x + 3017.147962 + x2 = -2411.714286 + 3017.147962 Reorder the terms: 3017.147962 + -109.8571429x + x2 = -2411.714286 + 3017.147962 Combine like terms: -2411.714286 + 3017.147962 = 605.433676 3017.147962 + -109.8571429x + x2 = 605.433676 Factor a perfect square on the left side: (x + -54.92857145)(x + -54.92857145) = 605.433676 Calculate the square root of the right side: 24.605561892 Break this problem into two subproblems by setting (x + -54.92857145) equal to 24.605561892 and -24.605561892.Subproblem 1
x + -54.92857145 = 24.605561892 Simplifying x + -54.92857145 = 24.605561892 Reorder the terms: -54.92857145 + x = 24.605561892 Solving -54.92857145 + x = 24.605561892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54.92857145' to each side of the equation. -54.92857145 + 54.92857145 + x = 24.605561892 + 54.92857145 Combine like terms: -54.92857145 + 54.92857145 = 0.00000000 0.00000000 + x = 24.605561892 + 54.92857145 x = 24.605561892 + 54.92857145 Combine like terms: 24.605561892 + 54.92857145 = 79.534133342 x = 79.534133342 Simplifying x = 79.534133342Subproblem 2
x + -54.92857145 = -24.605561892 Simplifying x + -54.92857145 = -24.605561892 Reorder the terms: -54.92857145 + x = -24.605561892 Solving -54.92857145 + x = -24.605561892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54.92857145' to each side of the equation. -54.92857145 + 54.92857145 + x = -24.605561892 + 54.92857145 Combine like terms: -54.92857145 + 54.92857145 = 0.00000000 0.00000000 + x = -24.605561892 + 54.92857145 x = -24.605561892 + 54.92857145 Combine like terms: -24.605561892 + 54.92857145 = 30.323009558 x = 30.323009558 Simplifying x = 30.323009558Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.534133342, 30.323009558}
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