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Simplifying 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 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 = 4.87192437Subproblem 2
x + -2.333333334 = -2.538591036 Simplifying 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 = -0.205257702Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.87192437, -0.205257702}
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