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Simplifying 12x2 + 6x + -3 = 0 Reorder the terms: -3 + 6x + 12x2 = 0 Solving -3 + 6x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 2x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + 4x2 = 0 Solving -1 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.5x + x2 = 0 + 0.25 0.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.5x + x2 = 0.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.25 + 0.0625 Combine like terms: 0.25 + 0.0625 = 0.3125 0.0625 + 0.5x + x2 = 0.3125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + 0.25) equal to 0.559016994 and -0.559016994.Subproblem 1
x + 0.25 = 0.559016994 Simplifying x + 0.25 = 0.559016994 Reorder the terms: 0.25 + x = 0.559016994 Solving 0.25 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.559016994 + -0.25 x = 0.559016994 + -0.25 Combine like terms: 0.559016994 + -0.25 = 0.309016994 x = 0.309016994 Simplifying x = 0.309016994Subproblem 2
x + 0.25 = -0.559016994 Simplifying x + 0.25 = -0.559016994 Reorder the terms: 0.25 + x = -0.559016994 Solving 0.25 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.559016994 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.559016994 + -0.25 x = -0.559016994 + -0.25 Combine like terms: -0.559016994 + -0.25 = -0.809016994 x = -0.809016994 Simplifying x = -0.809016994Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.309016994, -0.809016994}Solution
x = {0.309016994, -0.809016994}
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