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Simplifying 5 = -250x2 + 1250x Reorder the terms: 5 = 1250x + -250x2 Solving 5 = 1250x + -250x2 Solving for variable 'x'. Reorder the terms: 5 + -1250x + 250x2 = 1250x + -1250x + -250x2 + 250x2 Combine like terms: 1250x + -1250x = 0 5 + -1250x + 250x2 = 0 + -250x2 + 250x2 5 + -1250x + 250x2 = -250x2 + 250x2 Combine like terms: -250x2 + 250x2 = 0 5 + -1250x + 250x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -250x + 50x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -250x + 50x2)' equal to zero and attempt to solve: Simplifying 1 + -250x + 50x2 = 0 Solving 1 + -250x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.02 + -5x + x2 = 0.0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -5x + -0.02 + x2 = 0.0 + -0.02 Reorder the terms: 0.02 + -0.02 + -5x + x2 = 0.0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -5x + x2 = 0.0 + -0.02 -5x + x2 = 0.0 + -0.02 Combine like terms: 0.0 + -0.02 = -0.02 -5x + x2 = -0.02 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.02 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.02 + 6.25 Combine like terms: -0.02 + 6.25 = 6.23 6.25 + -5x + x2 = 6.23 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.23 Calculate the square root of the right side: 2.495996795 Break this problem into two subproblems by setting (x + -2.5) equal to 2.495996795 and -2.495996795.Subproblem 1
x + -2.5 = 2.495996795 Simplifying x + -2.5 = 2.495996795 Reorder the terms: -2.5 + x = 2.495996795 Solving -2.5 + x = 2.495996795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.495996795 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.495996795 + 2.5 x = 2.495996795 + 2.5 Combine like terms: 2.495996795 + 2.5 = 4.995996795 x = 4.995996795 Simplifying x = 4.995996795Subproblem 2
x + -2.5 = -2.495996795 Simplifying x + -2.5 = -2.495996795 Reorder the terms: -2.5 + x = -2.495996795 Solving -2.5 + x = -2.495996795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.495996795 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.495996795 + 2.5 x = -2.495996795 + 2.5 Combine like terms: -2.495996795 + 2.5 = 0.004003205 x = 0.004003205 Simplifying x = 0.004003205Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.995996795, 0.004003205}Solution
x = {4.995996795, 0.004003205}
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