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Simplifying x2 + -6x + 9 = 4x2 + 8x + 1 Reorder the terms: 9 + -6x + x2 = 4x2 + 8x + 1 Reorder the terms: 9 + -6x + x2 = 1 + 8x + 4x2 Solving 9 + -6x + x2 = 1 + 8x + 4x2 Solving for variable 'x'. Reorder the terms: 9 + -1 + -6x + -8x + x2 + -4x2 = 1 + 8x + 4x2 + -1 + -8x + -4x2 Combine like terms: 9 + -1 = 8 8 + -6x + -8x + x2 + -4x2 = 1 + 8x + 4x2 + -1 + -8x + -4x2 Combine like terms: -6x + -8x = -14x 8 + -14x + x2 + -4x2 = 1 + 8x + 4x2 + -1 + -8x + -4x2 Combine like terms: x2 + -4x2 = -3x2 8 + -14x + -3x2 = 1 + 8x + 4x2 + -1 + -8x + -4x2 Reorder the terms: 8 + -14x + -3x2 = 1 + -1 + 8x + -8x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 8 + -14x + -3x2 = 0 + 8x + -8x + 4x2 + -4x2 8 + -14x + -3x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 8 + -14x + -3x2 = 0 + 4x2 + -4x2 8 + -14x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + -14x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 4.666666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 4.666666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 2.666666667 4.666666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 4.666666667x + x2 = 2.666666667 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 = 2.666666667 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 2.666666667 + 5.444444448 Combine like terms: 2.666666667 + 5.444444448 = 8.111111115 5.444444448 + 4.666666667x + x2 = 8.111111115 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 8.111111115 Calculate the square root of the right side: 2.848001249 Break this problem into two subproblems by setting (x + 2.333333334) equal to 2.848001249 and -2.848001249.Subproblem 1
x + 2.333333334 = 2.848001249 Simplifying x + 2.333333334 = 2.848001249 Reorder the terms: 2.333333334 + x = 2.848001249 Solving 2.333333334 + x = 2.848001249 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 = 2.848001249 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 2.848001249 + -2.333333334 x = 2.848001249 + -2.333333334 Combine like terms: 2.848001249 + -2.333333334 = 0.514667915 x = 0.514667915 Simplifying x = 0.514667915Subproblem 2
x + 2.333333334 = -2.848001249 Simplifying x + 2.333333334 = -2.848001249 Reorder the terms: 2.333333334 + x = -2.848001249 Solving 2.333333334 + x = -2.848001249 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 = -2.848001249 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -2.848001249 + -2.333333334 x = -2.848001249 + -2.333333334 Combine like terms: -2.848001249 + -2.333333334 = -5.181334583 x = -5.181334583 Simplifying x = -5.181334583Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.514667915, -5.181334583}
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