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Simplifying 2x2 + 12x = 66 Reorder the terms: 12x + 2x2 = 66 Solving 12x + 2x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + 12x + 2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 6x + x2)' equal to zero and attempt to solve: Simplifying -33 + 6x + x2 = 0 Solving -33 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 6x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 6x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 6x + x2 = 0 + 33 6x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 6x + x2 = 33 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 = 33 + 9 Reorder the terms: 9 + 6x + x2 = 33 + 9 Combine like terms: 33 + 9 = 42 9 + 6x + x2 = 42 Factor a perfect square on the left side: (x + 3)(x + 3) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 3) equal to 6.480740698 and -6.480740698.Subproblem 1
x + 3 = 6.480740698 Simplifying x + 3 = 6.480740698 Reorder the terms: 3 + x = 6.480740698 Solving 3 + x = 6.480740698 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 = 6.480740698 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.480740698 + -3 x = 6.480740698 + -3 Combine like terms: 6.480740698 + -3 = 3.480740698 x = 3.480740698 Simplifying x = 3.480740698Subproblem 2
x + 3 = -6.480740698 Simplifying x + 3 = -6.480740698 Reorder the terms: 3 + x = -6.480740698 Solving 3 + x = -6.480740698 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 = -6.480740698 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.480740698 + -3 x = -6.480740698 + -3 Combine like terms: -6.480740698 + -3 = -9.480740698 x = -9.480740698 Simplifying x = -9.480740698Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.480740698, -9.480740698}Solution
x = {3.480740698, -9.480740698}
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