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Simplifying 12x2 + 2x + -6 = 0 Reorder the terms: -6 + 2x + 12x2 = 0 Solving -6 + 2x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + x + 6x2 = 0 Solving -3 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.1666666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.1666666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + 0.5 0.1666666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.1666666667x + x2 = 0.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = 0.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 0.25 + 0.1666666667x + x2 = 0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + 0.5) equal to 0.866025404 and -0.866025404.Subproblem 1
x + 0.5 = 0.866025404 Simplifying x + 0.5 = 0.866025404 Reorder the terms: 0.5 + x = 0.866025404 Solving 0.5 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.866025404 + -0.5 x = 0.866025404 + -0.5 Combine like terms: 0.866025404 + -0.5 = 0.366025404 x = 0.366025404 Simplifying x = 0.366025404Subproblem 2
x + 0.5 = -0.866025404 Simplifying x + 0.5 = -0.866025404 Reorder the terms: 0.5 + x = -0.866025404 Solving 0.5 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.866025404 + -0.5 x = -0.866025404 + -0.5 Combine like terms: -0.866025404 + -0.5 = -1.366025404 x = -1.366025404 Simplifying x = -1.366025404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.366025404, -1.366025404}Solution
x = {0.366025404, -1.366025404}
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