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Simplifying -36x2 + 96x + 3 = 0 Reorder the terms: 3 + 96x + -36x2 = 0 Solving 3 + 96x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 32x + -12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 32x + -12x2)' equal to zero and attempt to solve: Simplifying 1 + 32x + -12x2 = 0 Solving 1 + 32x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -2.666666667x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -2.666666667x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -2.666666667x + x2 = 0 + 0.08333333333 -2.666666667x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -2.666666667x + x2 = 0.08333333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.08333333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.08333333333 + 1.777777780 Combine like terms: 0.08333333333 + 1.777777780 = 1.86111111333 1.777777780 + -2.666666667x + x2 = 1.86111111333 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.86111111333 Calculate the square root of the right side: 1.364225463 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.364225463 and -1.364225463.Subproblem 1
x + -1.333333334 = 1.364225463 Simplifying x + -1.333333334 = 1.364225463 Reorder the terms: -1.333333334 + x = 1.364225463 Solving -1.333333334 + x = 1.364225463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.364225463 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.364225463 + 1.333333334 x = 1.364225463 + 1.333333334 Combine like terms: 1.364225463 + 1.333333334 = 2.697558797 x = 2.697558797 Simplifying x = 2.697558797Subproblem 2
x + -1.333333334 = -1.364225463 Simplifying x + -1.333333334 = -1.364225463 Reorder the terms: -1.333333334 + x = -1.364225463 Solving -1.333333334 + x = -1.364225463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.364225463 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.364225463 + 1.333333334 x = -1.364225463 + 1.333333334 Combine like terms: -1.364225463 + 1.333333334 = -0.030892129 x = -0.030892129 Simplifying x = -0.030892129Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.697558797, -0.030892129}Solution
x = {2.697558797, -0.030892129}
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