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Simplifying 0 = 4x2 + -445x + 5000 Reorder the terms: 0 = 5000 + -445x + 4x2 Solving 0 = 5000 + -445x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -5000 = -5000 -5000 + 445x + -4x2 = 5000 + -445x + 4x2 + -5000 + 445x + -4x2 Reorder the terms: -5000 + 445x + -4x2 = 5000 + -5000 + -445x + 445x + 4x2 + -4x2 Combine like terms: 5000 + -5000 = 0 -5000 + 445x + -4x2 = 0 + -445x + 445x + 4x2 + -4x2 -5000 + 445x + -4x2 = -445x + 445x + 4x2 + -4x2 Combine like terms: -445x + 445x = 0 -5000 + 445x + -4x2 = 0 + 4x2 + -4x2 -5000 + 445x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5000 + 445x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1250 + -111.25x + x2 = 0 Move the constant term to the right: Add '-1250' to each side of the equation. 1250 + -111.25x + -1250 + x2 = 0 + -1250 Reorder the terms: 1250 + -1250 + -111.25x + x2 = 0 + -1250 Combine like terms: 1250 + -1250 = 0 0 + -111.25x + x2 = 0 + -1250 -111.25x + x2 = 0 + -1250 Combine like terms: 0 + -1250 = -1250 -111.25x + x2 = -1250 The x term is -111.25x. Take half its coefficient (-55.625). Square it (3094.140625) and add it to both sides. Add '3094.140625' to each side of the equation. -111.25x + 3094.140625 + x2 = -1250 + 3094.140625 Reorder the terms: 3094.140625 + -111.25x + x2 = -1250 + 3094.140625 Combine like terms: -1250 + 3094.140625 = 1844.140625 3094.140625 + -111.25x + x2 = 1844.140625 Factor a perfect square on the left side: (x + -55.625)(x + -55.625) = 1844.140625 Calculate the square root of the right side: 42.943458466 Break this problem into two subproblems by setting (x + -55.625) equal to 42.943458466 and -42.943458466.Subproblem 1
x + -55.625 = 42.943458466 Simplifying x + -55.625 = 42.943458466 Reorder the terms: -55.625 + x = 42.943458466 Solving -55.625 + x = 42.943458466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.625' to each side of the equation. -55.625 + 55.625 + x = 42.943458466 + 55.625 Combine like terms: -55.625 + 55.625 = 0.000 0.000 + x = 42.943458466 + 55.625 x = 42.943458466 + 55.625 Combine like terms: 42.943458466 + 55.625 = 98.568458466 x = 98.568458466 Simplifying x = 98.568458466Subproblem 2
x + -55.625 = -42.943458466 Simplifying x + -55.625 = -42.943458466 Reorder the terms: -55.625 + x = -42.943458466 Solving -55.625 + x = -42.943458466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.625' to each side of the equation. -55.625 + 55.625 + x = -42.943458466 + 55.625 Combine like terms: -55.625 + 55.625 = 0.000 0.000 + x = -42.943458466 + 55.625 x = -42.943458466 + 55.625 Combine like terms: -42.943458466 + 55.625 = 12.681541534 x = 12.681541534 Simplifying x = 12.681541534Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.568458466, 12.681541534}
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