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Simplifying 6x2 + 99x + 108 = 0 Reorder the terms: 108 + 99x + 6x2 = 0 Solving 108 + 99x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(36 + 33x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(36 + 33x + 2x2)' equal to zero and attempt to solve: Simplifying 36 + 33x + 2x2 = 0 Solving 36 + 33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 18 + 16.5x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + 16.5x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 16.5x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 16.5x + x2 = 0 + -18 16.5x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 16.5x + x2 = -18 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = -18 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = -18 + 68.0625 Combine like terms: -18 + 68.0625 = 50.0625 68.0625 + 16.5x + x2 = 50.0625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (x + 8.25) equal to 7.075485849 and -7.075485849.Subproblem 1
x + 8.25 = 7.075485849 Simplifying x + 8.25 = 7.075485849 Reorder the terms: 8.25 + x = 7.075485849 Solving 8.25 + x = 7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 7.075485849 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 7.075485849 + -8.25 x = 7.075485849 + -8.25 Combine like terms: 7.075485849 + -8.25 = -1.174514151 x = -1.174514151 Simplifying x = -1.174514151Subproblem 2
x + 8.25 = -7.075485849 Simplifying x + 8.25 = -7.075485849 Reorder the terms: 8.25 + x = -7.075485849 Solving 8.25 + x = -7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -7.075485849 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -7.075485849 + -8.25 x = -7.075485849 + -8.25 Combine like terms: -7.075485849 + -8.25 = -15.325485849 x = -15.325485849 Simplifying x = -15.325485849Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.174514151, -15.325485849}Solution
x = {-1.174514151, -15.325485849}
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