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Simplifying -22 + -8x = -6x(x + 6) Reorder the terms: -22 + -8x = -6x(6 + x) -22 + -8x = (6 * -6x + x * -6x) -22 + -8x = (-36x + -6x2) Solving -22 + -8x = -36x + -6x2 Solving for variable 'x'. Combine like terms: -8x + 36x = 28x -22 + 28x + 6x2 = -36x + -6x2 + 36x + 6x2 Reorder the terms: -22 + 28x + 6x2 = -36x + 36x + -6x2 + 6x2 Combine like terms: -36x + 36x = 0 -22 + 28x + 6x2 = 0 + -6x2 + 6x2 -22 + 28x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -22 + 28x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 14x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -11 + 14x + 3x2 = 0 Solving -11 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 4.666666667x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 4.666666667x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + 3.666666667 4.666666667x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 4.666666667x + x2 = 3.666666667 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 = 3.666666667 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 3.666666667 + 5.444444448 Combine like terms: 3.666666667 + 5.444444448 = 9.111111115 5.444444448 + 4.666666667x + x2 = 9.111111115 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 9.111111115 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + 2.333333334) equal to 3.018461713 and -3.018461713.Subproblem 1
x + 2.333333334 = 3.018461713 Simplifying x + 2.333333334 = 3.018461713 Reorder the terms: 2.333333334 + x = 3.018461713 Solving 2.333333334 + x = 3.018461713 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 = 3.018461713 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.018461713 + -2.333333334 x = 3.018461713 + -2.333333334 Combine like terms: 3.018461713 + -2.333333334 = 0.685128379 x = 0.685128379 Simplifying x = 0.685128379Subproblem 2
x + 2.333333334 = -3.018461713 Simplifying x + 2.333333334 = -3.018461713 Reorder the terms: 2.333333334 + x = -3.018461713 Solving 2.333333334 + x = -3.018461713 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 = -3.018461713 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.018461713 + -2.333333334 x = -3.018461713 + -2.333333334 Combine like terms: -3.018461713 + -2.333333334 = -5.351795047 x = -5.351795047 Simplifying x = -5.351795047Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.685128379, -5.351795047}Solution
x = {0.685128379, -5.351795047}
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