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Simplifying 0 = 4x2 + 24x + 6 Reorder the terms: 0 = 6 + 24x + 4x2 Solving 0 = 6 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -24x + -4x2 = 6 + 24x + 4x2 + -6 + -24x + -4x2 Reorder the terms: -6 + -24x + -4x2 = 6 + -6 + 24x + -24x + 4x2 + -4x2 Combine like terms: 6 + -6 = 0 -6 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 -6 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -6 + -24x + -4x2 = 0 + 4x2 + -4x2 -6 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -6 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 12x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 12x + 2x2 = 0 Solving 3 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 6x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 6x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 6x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 6x + x2 = 0 + -1.5 6x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 6x + x2 = -1.5 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 = -1.5 + 9 Reorder the terms: 9 + 6x + x2 = -1.5 + 9 Combine like terms: -1.5 + 9 = 7.5 9 + 6x + x2 = 7.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 3) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 3 = 2.738612788 Simplifying x + 3 = 2.738612788 Reorder the terms: 3 + x = 2.738612788 Solving 3 + x = 2.738612788 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 = 2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.738612788 + -3 x = 2.738612788 + -3 Combine like terms: 2.738612788 + -3 = -0.261387212 x = -0.261387212 Simplifying x = -0.261387212Subproblem 2
x + 3 = -2.738612788 Simplifying x + 3 = -2.738612788 Reorder the terms: 3 + x = -2.738612788 Solving 3 + x = -2.738612788 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 = -2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.738612788 + -3 x = -2.738612788 + -3 Combine like terms: -2.738612788 + -3 = -5.738612788 x = -5.738612788 Simplifying x = -5.738612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.261387212, -5.738612788}Solution
x = {-0.261387212, -5.738612788}
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