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Simplifying 6x2 + 36x + 12 = 0 Reorder the terms: 12 + 36x + 6x2 = 0 Solving 12 + 36x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + 6x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + 6x + x2)' equal to zero and attempt to solve: Simplifying 2 + 6x + x2 = 0 Solving 2 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6x + x2 = 0 + -2 6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 6x + x2 = -2 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 = -2 + 9 Reorder the terms: 9 + 6x + x2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6x + x2 = 7 Factor a perfect square on the left side: (x + 3)(x + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 3 = 2.645751311 Simplifying x + 3 = 2.645751311 Reorder the terms: 3 + x = 2.645751311 Solving 3 + x = 2.645751311 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 = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.645751311 + -3 x = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 x = -0.354248689 Simplifying x = -0.354248689Subproblem 2
x + 3 = -2.645751311 Simplifying x + 3 = -2.645751311 Reorder the terms: 3 + x = -2.645751311 Solving 3 + x = -2.645751311 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 = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.645751311 + -3 x = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 x = -5.645751311 Simplifying x = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.354248689, -5.645751311}Solution
x = {-0.354248689, -5.645751311}
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