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Simplifying 3.5x2 + 364x + -6100.5 = 5135.5 Reorder the terms: -6100.5 + 364x + 3.5x2 = 5135.5 Solving -6100.5 + 364x + 3.5x2 = 5135.5 Solving for variable 'x'. Reorder the terms: -6100.5 + -5135.5 + 364x + 3.5x2 = 5135.5 + -5135.5 Combine like terms: -6100.5 + -5135.5 = -11236 -11236 + 364x + 3.5x2 = 5135.5 + -5135.5 Combine like terms: 5135.5 + -5135.5 = 0.0 -11236 + 364x + 3.5x2 = 0.0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -3210.285714 + 104x + x2 = 0 Move the constant term to the right: Add '3210.285714' to each side of the equation. -3210.285714 + 104x + 3210.285714 + x2 = 0 + 3210.285714 Reorder the terms: -3210.285714 + 3210.285714 + 104x + x2 = 0 + 3210.285714 Combine like terms: -3210.285714 + 3210.285714 = 0.000000 0.000000 + 104x + x2 = 0 + 3210.285714 104x + x2 = 0 + 3210.285714 Combine like terms: 0 + 3210.285714 = 3210.285714 104x + x2 = 3210.285714 The x term is 104x. Take half its coefficient (52). Square it (2704) and add it to both sides. Add '2704' to each side of the equation. 104x + 2704 + x2 = 3210.285714 + 2704 Reorder the terms: 2704 + 104x + x2 = 3210.285714 + 2704 Combine like terms: 3210.285714 + 2704 = 5914.285714 2704 + 104x + x2 = 5914.285714 Factor a perfect square on the left side: (x + 52)(x + 52) = 5914.285714 Calculate the square root of the right side: 76.904393334 Break this problem into two subproblems by setting (x + 52) equal to 76.904393334 and -76.904393334.Subproblem 1
x + 52 = 76.904393334 Simplifying x + 52 = 76.904393334 Reorder the terms: 52 + x = 76.904393334 Solving 52 + x = 76.904393334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -52 + x = 76.904393334 + -52 Combine like terms: 52 + -52 = 0 0 + x = 76.904393334 + -52 x = 76.904393334 + -52 Combine like terms: 76.904393334 + -52 = 24.904393334 x = 24.904393334 Simplifying x = 24.904393334Subproblem 2
x + 52 = -76.904393334 Simplifying x + 52 = -76.904393334 Reorder the terms: 52 + x = -76.904393334 Solving 52 + x = -76.904393334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -52 + x = -76.904393334 + -52 Combine like terms: 52 + -52 = 0 0 + x = -76.904393334 + -52 x = -76.904393334 + -52 Combine like terms: -76.904393334 + -52 = -128.904393334 x = -128.904393334 Simplifying x = -128.904393334Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.904393334, -128.904393334}
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