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Simplifying 144x2 + -528x + 114 = 0 Reorder the terms: 114 + -528x + 144x2 = 0 Solving 114 + -528x + 144x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(19 + -88x + 24x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(19 + -88x + 24x2)' equal to zero and attempt to solve: Simplifying 19 + -88x + 24x2 = 0 Solving 19 + -88x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.7916666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-0.7916666667' to each side of the equation. 0.7916666667 + -3.666666667x + -0.7916666667 + x2 = 0 + -0.7916666667 Reorder the terms: 0.7916666667 + -0.7916666667 + -3.666666667x + x2 = 0 + -0.7916666667 Combine like terms: 0.7916666667 + -0.7916666667 = 0.0000000000 0.0000000000 + -3.666666667x + x2 = 0 + -0.7916666667 -3.666666667x + x2 = 0 + -0.7916666667 Combine like terms: 0 + -0.7916666667 = -0.7916666667 -3.666666667x + x2 = -0.7916666667 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 = -0.7916666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -0.7916666667 + 3.361111114 Combine like terms: -0.7916666667 + 3.361111114 = 2.5694444473 3.361111114 + -3.666666667x + x2 = 2.5694444473 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 2.5694444473 Calculate the square root of the right side: 1.602948673 Break this problem into two subproblems by setting (x + -1.833333334) equal to 1.602948673 and -1.602948673.Subproblem 1
x + -1.833333334 = 1.602948673 Simplifying x + -1.833333334 = 1.602948673 Reorder the terms: -1.833333334 + x = 1.602948673 Solving -1.833333334 + x = 1.602948673 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 = 1.602948673 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 1.602948673 + 1.833333334 x = 1.602948673 + 1.833333334 Combine like terms: 1.602948673 + 1.833333334 = 3.436282007 x = 3.436282007 Simplifying x = 3.436282007Subproblem 2
x + -1.833333334 = -1.602948673 Simplifying x + -1.833333334 = -1.602948673 Reorder the terms: -1.833333334 + x = -1.602948673 Solving -1.833333334 + x = -1.602948673 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 = -1.602948673 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -1.602948673 + 1.833333334 x = -1.602948673 + 1.833333334 Combine like terms: -1.602948673 + 1.833333334 = 0.230384661 x = 0.230384661 Simplifying x = 0.230384661Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.436282007, 0.230384661}Solution
x = {3.436282007, 0.230384661}
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