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Simplifying 6x2 + 36x + 51 = 0 Reorder the terms: 51 + 36x + 6x2 = 0 Solving 51 + 36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(17 + 12x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(17 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 17 + 12x + 2x2 = 0 Solving 17 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 6x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 6x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 6x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 6x + x2 = 0 + -8.5 6x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 6x + x2 = -8.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -8.5 + 9 Reorder the terms: 9 + 6x + x2 = -8.5 + 9 Combine like terms: -8.5 + 9 = 0.5 9 + 6x + x2 = 0.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 3) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 3 = 0.707106781 Simplifying x + 3 = 0.707106781 Reorder the terms: 3 + x = 0.707106781 Solving 3 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0.707106781 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.707106781 + -3 x = 0.707106781 + -3 Combine like terms: 0.707106781 + -3 = -2.292893219 x = -2.292893219 Simplifying x = -2.292893219Subproblem 2
x + 3 = -0.707106781 Simplifying x + 3 = -0.707106781 Reorder the terms: 3 + x = -0.707106781 Solving 3 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -0.707106781 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.707106781 + -3 x = -0.707106781 + -3 Combine like terms: -0.707106781 + -3 = -3.707106781 x = -3.707106781 Simplifying x = -3.707106781Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.292893219, -3.707106781}Solution
x = {-2.292893219, -3.707106781}
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