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Simplifying 6x2 + 33x + -9 = 0 Reorder the terms: -9 + 33x + 6x2 = 0 Solving -9 + 33x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 11x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 11x + 2x2 = 0 Solving -3 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 5.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 5.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 5.5x + x2 = 0 + 1.5 5.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 5.5x + x2 = 1.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 1.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 1.5 + 7.5625 Combine like terms: 1.5 + 7.5625 = 9.0625 7.5625 + 5.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 2.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 2.75 = 3.010398645 Simplifying x + 2.75 = 3.010398645 Reorder the terms: 2.75 + x = 3.010398645 Solving 2.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.010398645 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.010398645 + -2.75 x = 3.010398645 + -2.75 Combine like terms: 3.010398645 + -2.75 = 0.260398645 x = 0.260398645 Simplifying x = 0.260398645Subproblem 2
x + 2.75 = -3.010398645 Simplifying x + 2.75 = -3.010398645 Reorder the terms: 2.75 + x = -3.010398645 Solving 2.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.010398645 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.010398645 + -2.75 x = -3.010398645 + -2.75 Combine like terms: -3.010398645 + -2.75 = -5.760398645 x = -5.760398645 Simplifying x = -5.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.260398645, -5.760398645}Solution
x = {0.260398645, -5.760398645}
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