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Simplifying -6x2 + 52x + 90 = 0 Reorder the terms: 90 + 52x + -6x2 = 0 Solving 90 + 52x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + 26x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + 26x + -3x2)' equal to zero and attempt to solve: Simplifying 45 + 26x + -3x2 = 0 Solving 45 + 26x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -15 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -8.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -8.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8.666666667x + x2 = 0 + 15 -8.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8.666666667x + x2 = 15 The x term is -8.666666667x. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667x + 18.77777778 + x2 = 15 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = 15 + 18.77777778 Combine like terms: 15 + 18.77777778 = 33.77777778 18.77777778 + -8.666666667x + x2 = 33.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 33.77777778 Calculate the square root of the right side: 5.811865258 Break this problem into two subproblems by setting (x + -4.333333334) equal to 5.811865258 and -5.811865258.Subproblem 1
x + -4.333333334 = 5.811865258 Simplifying x + -4.333333334 = 5.811865258 Reorder the terms: -4.333333334 + x = 5.811865258 Solving -4.333333334 + x = 5.811865258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 5.811865258 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 5.811865258 + 4.333333334 x = 5.811865258 + 4.333333334 Combine like terms: 5.811865258 + 4.333333334 = 10.145198592 x = 10.145198592 Simplifying x = 10.145198592Subproblem 2
x + -4.333333334 = -5.811865258 Simplifying x + -4.333333334 = -5.811865258 Reorder the terms: -4.333333334 + x = -5.811865258 Solving -4.333333334 + x = -5.811865258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -5.811865258 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -5.811865258 + 4.333333334 x = -5.811865258 + 4.333333334 Combine like terms: -5.811865258 + 4.333333334 = -1.478531924 x = -1.478531924 Simplifying x = -1.478531924Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.145198592, -1.478531924}Solution
x = {10.145198592, -1.478531924}
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