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Simplifying (3x2) + (14x) + -1(3) = 0 Multiply -1 * 3 (3x2) + (14x) + -3 = 0 Reorder the terms: -3 + (14x) + (3x2) = 0 Solving -3 + (14x) + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + (4.666666667x) + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + (4.666666667x) + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + (4.666666667x) + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + (4.666666667x) + x2 = 0 + 1 (4.666666667x) + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 (4.666666667x) + x2 = 1 The x term is (4.666666667x). Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. (4.666666667x) + 5.444444448 + x2 = 1 + 5.444444448 Reorder the terms: 5.444444448 + (4.666666667x) + x2 = 1 + 5.444444448 Combine like terms: 1 + 5.444444448 = 6.444444448 5.444444448 + (4.666666667x) + x2 = 6.444444448 Factor a perfect square on the left side: ((x) + 2.333333334)((x) + 2.333333334) = 6.444444448 Calculate the square root of the right side: 2.538591036 Break this problem into two subproblems by setting ((x) + 2.333333334) equal to 2.538591036 and -2.538591036.Subproblem 1
(x) + 2.333333334 = 2.538591036 Simplifying (x) + 2.333333334 = 2.538591036 x + 2.333333334 = 2.538591036 Reorder the terms: 2.333333334 + x = 2.538591036 Solving 2.333333334 + x = 2.538591036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 2.538591036 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.538591036 + -2.333333334 x = 2.538591036 + -2.333333334 Combine like terms: 2.538591036 + -2.333333334 = 0.205257702 x = 0.205257702 Simplifying x = 0.205257702Subproblem 2
(x) + 2.333333334 = -2.538591036 Simplifying (x) + 2.333333334 = -2.538591036 x + 2.333333334 = -2.538591036 Reorder the terms: 2.333333334 + x = -2.538591036 Solving 2.333333334 + x = -2.538591036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -2.538591036 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.538591036 + -2.333333334 x = -2.538591036 + -2.333333334 Combine like terms: -2.538591036 + -2.333333334 = -4.87192437 x = -4.87192437 Simplifying x = -4.87192437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.205257702, -4.87192437}
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