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Simplifying 3250x2 + 5489x + 5212 = 91000 Reorder the terms: 5212 + 5489x + 3250x2 = 91000 Solving 5212 + 5489x + 3250x2 = 91000 Solving for variable 'x'. Reorder the terms: 5212 + -91000 + 5489x + 3250x2 = 91000 + -91000 Combine like terms: 5212 + -91000 = -85788 -85788 + 5489x + 3250x2 = 91000 + -91000 Combine like terms: 91000 + -91000 = 0 -85788 + 5489x + 3250x2 = 0 Begin completing the square. Divide all terms by 3250 the coefficient of the squared term: Divide each side by '3250'. -26.39630769 + 1.688923077x + x2 = 0 Move the constant term to the right: Add '26.39630769' to each side of the equation. -26.39630769 + 1.688923077x + 26.39630769 + x2 = 0 + 26.39630769 Reorder the terms: -26.39630769 + 26.39630769 + 1.688923077x + x2 = 0 + 26.39630769 Combine like terms: -26.39630769 + 26.39630769 = 0.00000000 0.00000000 + 1.688923077x + x2 = 0 + 26.39630769 1.688923077x + x2 = 0 + 26.39630769 Combine like terms: 0 + 26.39630769 = 26.39630769 1.688923077x + x2 = 26.39630769 The x term is 1.688923077x. Take half its coefficient (0.8444615385). Square it (0.7131152900) and add it to both sides. Add '0.7131152900' to each side of the equation. 1.688923077x + 0.7131152900 + x2 = 26.39630769 + 0.7131152900 Reorder the terms: 0.7131152900 + 1.688923077x + x2 = 26.39630769 + 0.7131152900 Combine like terms: 26.39630769 + 0.7131152900 = 27.10942298 0.7131152900 + 1.688923077x + x2 = 27.10942298 Factor a perfect square on the left side: (x + 0.8444615385)(x + 0.8444615385) = 27.10942298 Calculate the square root of the right side: 5.206671007 Break this problem into two subproblems by setting (x + 0.8444615385) equal to 5.206671007 and -5.206671007.Subproblem 1
x + 0.8444615385 = 5.206671007 Simplifying x + 0.8444615385 = 5.206671007 Reorder the terms: 0.8444615385 + x = 5.206671007 Solving 0.8444615385 + x = 5.206671007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8444615385' to each side of the equation. 0.8444615385 + -0.8444615385 + x = 5.206671007 + -0.8444615385 Combine like terms: 0.8444615385 + -0.8444615385 = 0.0000000000 0.0000000000 + x = 5.206671007 + -0.8444615385 x = 5.206671007 + -0.8444615385 Combine like terms: 5.206671007 + -0.8444615385 = 4.3622094685 x = 4.3622094685 Simplifying x = 4.3622094685Subproblem 2
x + 0.8444615385 = -5.206671007 Simplifying x + 0.8444615385 = -5.206671007 Reorder the terms: 0.8444615385 + x = -5.206671007 Solving 0.8444615385 + x = -5.206671007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8444615385' to each side of the equation. 0.8444615385 + -0.8444615385 + x = -5.206671007 + -0.8444615385 Combine like terms: 0.8444615385 + -0.8444615385 = 0.0000000000 0.0000000000 + x = -5.206671007 + -0.8444615385 x = -5.206671007 + -0.8444615385 Combine like terms: -5.206671007 + -0.8444615385 = -6.0511325455 x = -6.0511325455 Simplifying x = -6.0511325455Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.3622094685, -6.0511325455}
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