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Simplifying 0 = 6x2 + -22x + -10 Reorder the terms: 0 = -10 + -22x + 6x2 Solving 0 = -10 + -22x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + 22x + -6x2 = -10 + -22x + 6x2 + 10 + 22x + -6x2 Reorder the terms: 10 + 22x + -6x2 = -10 + 10 + -22x + 22x + 6x2 + -6x2 Combine like terms: -10 + 10 = 0 10 + 22x + -6x2 = 0 + -22x + 22x + 6x2 + -6x2 10 + 22x + -6x2 = -22x + 22x + 6x2 + -6x2 Combine like terms: -22x + 22x = 0 10 + 22x + -6x2 = 0 + 6x2 + -6x2 10 + 22x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 10 + 22x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 11x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 11x + -3x2)' equal to zero and attempt to solve: Simplifying 5 + 11x + -3x2 = 0 Solving 5 + 11x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -3.666666667x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -3.666666667x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -3.666666667x + x2 = 0 + 1.666666667 -3.666666667x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -3.666666667x + x2 = 1.666666667 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 1.666666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 1.666666667 + 3.361111114 Combine like terms: 1.666666667 + 3.361111114 = 5.027777781 3.361111114 + -3.666666667x + x2 = 5.027777781 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 5.027777781 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.242270675 and -2.242270675.Subproblem 1
x + -1.833333334 = 2.242270675 Simplifying x + -1.833333334 = 2.242270675 Reorder the terms: -1.833333334 + x = 2.242270675 Solving -1.833333334 + x = 2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.242270675 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.242270675 + 1.833333334 x = 2.242270675 + 1.833333334 Combine like terms: 2.242270675 + 1.833333334 = 4.075604009 x = 4.075604009 Simplifying x = 4.075604009Subproblem 2
x + -1.833333334 = -2.242270675 Simplifying x + -1.833333334 = -2.242270675 Reorder the terms: -1.833333334 + x = -2.242270675 Solving -1.833333334 + x = -2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.242270675 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.242270675 + 1.833333334 x = -2.242270675 + 1.833333334 Combine like terms: -2.242270675 + 1.833333334 = -0.408937341 x = -0.408937341 Simplifying x = -0.408937341Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.075604009, -0.408937341}Solution
x = {4.075604009, -0.408937341}
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