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Simplifying 3x + -4 = 3x2 + -14.6x + -11.2 Reorder the terms: -4 + 3x = 3x2 + -14.6x + -11.2 Reorder the terms: -4 + 3x = -11.2 + -14.6x + 3x2 Solving -4 + 3x = -11.2 + -14.6x + 3x2 Solving for variable 'x'. Reorder the terms: -4 + 11.2 + 3x + 14.6x + -3x2 = -11.2 + -14.6x + 3x2 + 11.2 + 14.6x + -3x2 Combine like terms: -4 + 11.2 = 7.2 7.2 + 3x + 14.6x + -3x2 = -11.2 + -14.6x + 3x2 + 11.2 + 14.6x + -3x2 Combine like terms: 3x + 14.6x = 17.6x 7.2 + 17.6x + -3x2 = -11.2 + -14.6x + 3x2 + 11.2 + 14.6x + -3x2 Reorder the terms: 7.2 + 17.6x + -3x2 = -11.2 + 11.2 + -14.6x + 14.6x + 3x2 + -3x2 Combine like terms: -11.2 + 11.2 = 0.0 7.2 + 17.6x + -3x2 = 0.0 + -14.6x + 14.6x + 3x2 + -3x2 7.2 + 17.6x + -3x2 = -14.6x + 14.6x + 3x2 + -3x2 Combine like terms: -14.6x + 14.6x = 0.0 7.2 + 17.6x + -3x2 = 0.0 + 3x2 + -3x2 7.2 + 17.6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 7.2 + 17.6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.4 + -5.866666667x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -5.866666667x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -5.866666667x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -5.866666667x + x2 = 0 + 2.4 -5.866666667x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -5.866666667x + x2 = 2.4 The x term is -5.866666667x. Take half its coefficient (-2.933333334). Square it (8.604444448) and add it to both sides. Add '8.604444448' to each side of the equation. -5.866666667x + 8.604444448 + x2 = 2.4 + 8.604444448 Reorder the terms: 8.604444448 + -5.866666667x + x2 = 2.4 + 8.604444448 Combine like terms: 2.4 + 8.604444448 = 11.004444448 8.604444448 + -5.866666667x + x2 = 11.004444448 Factor a perfect square on the left side: (x + -2.933333334)(x + -2.933333334) = 11.004444448 Calculate the square root of the right side: 3.317294748 Break this problem into two subproblems by setting (x + -2.933333334) equal to 3.317294748 and -3.317294748.Subproblem 1
x + -2.933333334 = 3.317294748 Simplifying x + -2.933333334 = 3.317294748 Reorder the terms: -2.933333334 + x = 3.317294748 Solving -2.933333334 + x = 3.317294748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.933333334' to each side of the equation. -2.933333334 + 2.933333334 + x = 3.317294748 + 2.933333334 Combine like terms: -2.933333334 + 2.933333334 = 0.000000000 0.000000000 + x = 3.317294748 + 2.933333334 x = 3.317294748 + 2.933333334 Combine like terms: 3.317294748 + 2.933333334 = 6.250628082 x = 6.250628082 Simplifying x = 6.250628082Subproblem 2
x + -2.933333334 = -3.317294748 Simplifying x + -2.933333334 = -3.317294748 Reorder the terms: -2.933333334 + x = -3.317294748 Solving -2.933333334 + x = -3.317294748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.933333334' to each side of the equation. -2.933333334 + 2.933333334 + x = -3.317294748 + 2.933333334 Combine like terms: -2.933333334 + 2.933333334 = 0.000000000 0.000000000 + x = -3.317294748 + 2.933333334 x = -3.317294748 + 2.933333334 Combine like terms: -3.317294748 + 2.933333334 = -0.383961414 x = -0.383961414 Simplifying x = -0.383961414Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.250628082, -0.383961414}
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