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Simplifying 12x2 + -46x + 16 = 0 Reorder the terms: 16 + -46x + 12x2 = 0 Solving 16 + -46x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -23x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -23x + 6x2)' equal to zero and attempt to solve: Simplifying 8 + -23x + 6x2 = 0 Solving 8 + -23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -3.833333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -3.833333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -3.833333333x + x2 = 0 + -1.333333333 -3.833333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -3.833333333x + x2 = -1.333333333 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = -1.333333333 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = -1.333333333 + 3.673611112 Combine like terms: -1.333333333 + 3.673611112 = 2.340277779 3.673611112 + -3.833333333x + x2 = 2.340277779 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 2.340277779 Calculate the square root of the right side: 1.529796646 Break this problem into two subproblems by setting (x + -1.916666667) equal to 1.529796646 and -1.529796646.Subproblem 1
x + -1.916666667 = 1.529796646 Simplifying x + -1.916666667 = 1.529796646 Reorder the terms: -1.916666667 + x = 1.529796646 Solving -1.916666667 + x = 1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 1.529796646 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 1.529796646 + 1.916666667 x = 1.529796646 + 1.916666667 Combine like terms: 1.529796646 + 1.916666667 = 3.446463313 x = 3.446463313 Simplifying x = 3.446463313Subproblem 2
x + -1.916666667 = -1.529796646 Simplifying x + -1.916666667 = -1.529796646 Reorder the terms: -1.916666667 + x = -1.529796646 Solving -1.916666667 + x = -1.529796646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -1.529796646 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -1.529796646 + 1.916666667 x = -1.529796646 + 1.916666667 Combine like terms: -1.529796646 + 1.916666667 = 0.386870021 x = 0.386870021 Simplifying x = 0.386870021Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.446463313, 0.386870021}Solution
x = {3.446463313, 0.386870021}
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