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Simplifying (27.821x2) + (139.25x) + 707 = 1300 Reorder the terms: 707 + (139.25x) + (27.821x2) = 1300 Solving 707 + (139.25x) + (27.821x2) = 1300 Solving for variable 'x'. Reorder the terms: 707 + -1300 + (139.25x) + (27.821x2) = 1300 + -1300 Combine like terms: 707 + -1300 = -593 -593 + (139.25x) + (27.821x2) = 1300 + -1300 Combine like terms: 1300 + -1300 = 0 -593 + (139.25x) + (27.821x2) = 0 Begin completing the square. Divide all terms by 27.821 the coefficient of the squared term: Divide each side by '27.821'. -21.31483412 + (5.00521189x) + x2 = 0 Move the constant term to the right: Add '21.31483412' to each side of the equation. -21.31483412 + (5.00521189x) + 21.31483412 + x2 = 0 + 21.31483412 Reorder the terms: -21.31483412 + 21.31483412 + (5.00521189x) + x2 = 0 + 21.31483412 Combine like terms: -21.31483412 + 21.31483412 = 0.00000000 0.00000000 + (5.00521189x) + x2 = 0 + 21.31483412 (5.00521189x) + x2 = 0 + 21.31483412 Combine like terms: 0 + 21.31483412 = 21.31483412 (5.00521189x) + x2 = 21.31483412 The x term is (5.00521189x). Take half its coefficient (2.502605945). Square it (6.263036516) and add it to both sides. Add '6.263036516' to each side of the equation. (5.00521189x) + 6.263036516 + x2 = 21.31483412 + 6.263036516 Reorder the terms: 6.263036516 + (5.00521189x) + x2 = 21.31483412 + 6.263036516 Combine like terms: 21.31483412 + 6.263036516 = 27.577870636 6.263036516 + (5.00521189x) + x2 = 27.577870636 Factor a perfect square on the left side: ((x) + 2.502605945)((x) + 2.502605945) = 27.577870636 Calculate the square root of the right side: 5.251463666 Break this problem into two subproblems by setting ((x) + 2.502605945) equal to 5.251463666 and -5.251463666.Subproblem 1
(x) + 2.502605945 = 5.251463666 Simplifying (x) + 2.502605945 = 5.251463666 x + 2.502605945 = 5.251463666 Reorder the terms: 2.502605945 + x = 5.251463666 Solving 2.502605945 + x = 5.251463666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.502605945' to each side of the equation. 2.502605945 + -2.502605945 + x = 5.251463666 + -2.502605945 Combine like terms: 2.502605945 + -2.502605945 = 0.000000000 0.000000000 + x = 5.251463666 + -2.502605945 x = 5.251463666 + -2.502605945 Combine like terms: 5.251463666 + -2.502605945 = 2.748857721 x = 2.748857721 Simplifying x = 2.748857721Subproblem 2
(x) + 2.502605945 = -5.251463666 Simplifying (x) + 2.502605945 = -5.251463666 x + 2.502605945 = -5.251463666 Reorder the terms: 2.502605945 + x = -5.251463666 Solving 2.502605945 + x = -5.251463666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.502605945' to each side of the equation. 2.502605945 + -2.502605945 + x = -5.251463666 + -2.502605945 Combine like terms: 2.502605945 + -2.502605945 = 0.000000000 0.000000000 + x = -5.251463666 + -2.502605945 x = -5.251463666 + -2.502605945 Combine like terms: -5.251463666 + -2.502605945 = -7.754069611 x = -7.754069611 Simplifying x = -7.754069611Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.748857721, -7.754069611}
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