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Simplifying 6000000000 = 3.15x2 + 24.4x + 780 Reorder the terms: 6000000000 = 780 + 24.4x + 3.15x2 Solving 6000000000 = 780 + 24.4x + 3.15x2 Solving for variable 'x'. Combine like terms: 6000000000 + -780 = 5999999220 5999999220 + -24.4x + -3.15x2 = 780 + 24.4x + 3.15x2 + -780 + -24.4x + -3.15x2 Reorder the terms: 5999999220 + -24.4x + -3.15x2 = 780 + -780 + 24.4x + -24.4x + 3.15x2 + -3.15x2 Combine like terms: 780 + -780 = 0 5999999220 + -24.4x + -3.15x2 = 0 + 24.4x + -24.4x + 3.15x2 + -3.15x2 5999999220 + -24.4x + -3.15x2 = 24.4x + -24.4x + 3.15x2 + -3.15x2 Combine like terms: 24.4x + -24.4x = 0.0 5999999220 + -24.4x + -3.15x2 = 0.0 + 3.15x2 + -3.15x2 5999999220 + -24.4x + -3.15x2 = 3.15x2 + -3.15x2 Combine like terms: 3.15x2 + -3.15x2 = 0.00 5999999220 + -24.4x + -3.15x2 = 0.00 Begin completing the square. Divide all terms by -3.15 the coefficient of the squared term: Divide each side by '-3.15'. -1904761657 + 7.746031746x + x2 = 0 Move the constant term to the right: Add '1904761657' to each side of the equation. -1904761657 + 7.746031746x + 1904761657 + x2 = 0 + 1904761657 Reorder the terms: -1904761657 + 1904761657 + 7.746031746x + x2 = 0 + 1904761657 Combine like terms: -1904761657 + 1904761657 = 0 0 + 7.746031746x + x2 = 0 + 1904761657 7.746031746x + x2 = 0 + 1904761657 Combine like terms: 0 + 1904761657 = 1904761657 7.746031746x + x2 = 1904761657 The x term is 7.746031746x. Take half its coefficient (3.873015873). Square it (15.00025195) and add it to both sides. Add '15.00025195' to each side of the equation. 7.746031746x + 15.00025195 + x2 = 1904761657 + 15.00025195 Reorder the terms: 15.00025195 + 7.746031746x + x2 = 1904761657 + 15.00025195 Combine like terms: 1904761657 + 15.00025195 = 1904761672.00025195 15.00025195 + 7.746031746x + x2 = 1904761672.00025195 Factor a perfect square on the left side: (x + 3.873015873)(x + 3.873015873) = 1904761672.00025195 Calculate the square root of the right side: 43643.575380579 Break this problem into two subproblems by setting (x + 3.873015873) equal to 43643.575380579 and -43643.575380579.Subproblem 1
x + 3.873015873 = 43643.575380579 Simplifying x + 3.873015873 = 43643.575380579 Reorder the terms: 3.873015873 + x = 43643.575380579 Solving 3.873015873 + x = 43643.575380579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.873015873' to each side of the equation. 3.873015873 + -3.873015873 + x = 43643.575380579 + -3.873015873 Combine like terms: 3.873015873 + -3.873015873 = 0.000000000 0.000000000 + x = 43643.575380579 + -3.873015873 x = 43643.575380579 + -3.873015873 Combine like terms: 43643.575380579 + -3.873015873 = 43639.702364706 x = 43639.702364706 Simplifying x = 43639.702364706Subproblem 2
x + 3.873015873 = -43643.575380579 Simplifying x + 3.873015873 = -43643.575380579 Reorder the terms: 3.873015873 + x = -43643.575380579 Solving 3.873015873 + x = -43643.575380579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.873015873' to each side of the equation. 3.873015873 + -3.873015873 + x = -43643.575380579 + -3.873015873 Combine like terms: 3.873015873 + -3.873015873 = 0.000000000 0.000000000 + x = -43643.575380579 + -3.873015873 x = -43643.575380579 + -3.873015873 Combine like terms: -43643.575380579 + -3.873015873 = -43647.448396452 x = -43647.448396452 Simplifying x = -43647.448396452Solution
The solution to the problem is based on the solutions from the subproblems. x = {43639.702364706, -43647.448396452}
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