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Simplifying 6x2 + 69x + 36 = 0 Reorder the terms: 36 + 69x + 6x2 = 0 Solving 36 + 69x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 23x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + 23x + 2x2)' equal to zero and attempt to solve: Simplifying 12 + 23x + 2x2 = 0 Solving 12 + 23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 11.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 11.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 11.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 11.5x + x2 = 0 + -6 11.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 11.5x + x2 = -6 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = -6 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = -6 + 33.0625 Combine like terms: -6 + 33.0625 = 27.0625 33.0625 + 11.5x + x2 = 27.0625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (x + 5.75) equal to 5.202163012 and -5.202163012.Subproblem 1
x + 5.75 = 5.202163012 Simplifying x + 5.75 = 5.202163012 Reorder the terms: 5.75 + x = 5.202163012 Solving 5.75 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 5.202163012 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 5.202163012 + -5.75 x = 5.202163012 + -5.75 Combine like terms: 5.202163012 + -5.75 = -0.547836988 x = -0.547836988 Simplifying x = -0.547836988Subproblem 2
x + 5.75 = -5.202163012 Simplifying x + 5.75 = -5.202163012 Reorder the terms: 5.75 + x = -5.202163012 Solving 5.75 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -5.202163012 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -5.202163012 + -5.75 x = -5.202163012 + -5.75 Combine like terms: -5.202163012 + -5.75 = -10.952163012 x = -10.952163012 Simplifying x = -10.952163012Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.547836988, -10.952163012}Solution
x = {-0.547836988, -10.952163012}
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