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Simplifying 6x2 + -46x + -60 = 0 Reorder the terms: -60 + -46x + 6x2 = 0 Solving -60 + -46x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -23x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -23x + 3x2)' equal to zero and attempt to solve: Simplifying -30 + -23x + 3x2 = 0 Solving -30 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -7.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -7.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7.666666667x + x2 = 0 + 10 -7.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -7.666666667x + x2 = 10 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 10 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 10 + 14.69444445 Combine like terms: 10 + 14.69444445 = 24.69444445 14.69444445 + -7.666666667x + x2 = 24.69444445 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 24.69444445 Calculate the square root of the right side: 4.969350506 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.969350506 and -4.969350506.Subproblem 1
x + -3.833333334 = 4.969350506 Simplifying x + -3.833333334 = 4.969350506 Reorder the terms: -3.833333334 + x = 4.969350506 Solving -3.833333334 + x = 4.969350506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.969350506 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.969350506 + 3.833333334 x = 4.969350506 + 3.833333334 Combine like terms: 4.969350506 + 3.833333334 = 8.80268384 x = 8.80268384 Simplifying x = 8.80268384Subproblem 2
x + -3.833333334 = -4.969350506 Simplifying x + -3.833333334 = -4.969350506 Reorder the terms: -3.833333334 + x = -4.969350506 Solving -3.833333334 + x = -4.969350506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.969350506 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.969350506 + 3.833333334 x = -4.969350506 + 3.833333334 Combine like terms: -4.969350506 + 3.833333334 = -1.136017172 x = -1.136017172 Simplifying x = -1.136017172Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.80268384, -1.136017172}Solution
x = {8.80268384, -1.136017172}
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