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Simplifying 2x2 + 14x + -4 = -1x2 + 3 Reorder the terms: -4 + 14x + 2x2 = -1x2 + 3 Reorder the terms: -4 + 14x + 2x2 = 3 + -1x2 Solving -4 + 14x + 2x2 = 3 + -1x2 Solving for variable 'x'. Reorder the terms: -4 + -3 + 14x + 2x2 + x2 = 3 + -1x2 + -3 + x2 Combine like terms: -4 + -3 = -7 -7 + 14x + 2x2 + x2 = 3 + -1x2 + -3 + x2 Combine like terms: 2x2 + x2 = 3x2 -7 + 14x + 3x2 = 3 + -1x2 + -3 + x2 Reorder the terms: -7 + 14x + 3x2 = 3 + -3 + -1x2 + x2 Combine like terms: 3 + -3 = 0 -7 + 14x + 3x2 = 0 + -1x2 + x2 -7 + 14x + 3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -7 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 4.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 4.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 2.333333333 4.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 4.666666667x + x2 = 2.333333333 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 = 2.333333333 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 2.333333333 + 5.444444448 Combine like terms: 2.333333333 + 5.444444448 = 7.777777781 5.444444448 + 4.666666667x + x2 = 7.777777781 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 7.777777781 Calculate the square root of the right side: 2.788866756 Break this problem into two subproblems by setting (x + 2.333333334) equal to 2.788866756 and -2.788866756.Subproblem 1
x + 2.333333334 = 2.788866756 Simplifying x + 2.333333334 = 2.788866756 Reorder the terms: 2.333333334 + x = 2.788866756 Solving 2.333333334 + x = 2.788866756 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 = 2.788866756 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.788866756 + -2.333333334 x = 2.788866756 + -2.333333334 Combine like terms: 2.788866756 + -2.333333334 = 0.455533422 x = 0.455533422 Simplifying x = 0.455533422Subproblem 2
x + 2.333333334 = -2.788866756 Simplifying x + 2.333333334 = -2.788866756 Reorder the terms: 2.333333334 + x = -2.788866756 Solving 2.333333334 + x = -2.788866756 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 = -2.788866756 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.788866756 + -2.333333334 x = -2.788866756 + -2.333333334 Combine like terms: -2.788866756 + -2.333333334 = -5.12220009 x = -5.12220009 Simplifying x = -5.12220009Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.455533422, -5.12220009}
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