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Simplifying 3x(4x + 22) = 3x + -4 Reorder the terms: 3x(22 + 4x) = 3x + -4 (22 * 3x + 4x * 3x) = 3x + -4 (66x + 12x2) = 3x + -4 Reorder the terms: 66x + 12x2 = -4 + 3x Solving 66x + 12x2 = -4 + 3x Solving for variable 'x'. Reorder the terms: 4 + 66x + -3x + 12x2 = -4 + 3x + 4 + -3x Combine like terms: 66x + -3x = 63x 4 + 63x + 12x2 = -4 + 3x + 4 + -3x Reorder the terms: 4 + 63x + 12x2 = -4 + 4 + 3x + -3x Combine like terms: -4 + 4 = 0 4 + 63x + 12x2 = 0 + 3x + -3x 4 + 63x + 12x2 = 3x + -3x Combine like terms: 3x + -3x = 0 4 + 63x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 5.25x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 5.25x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 5.25x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 5.25x + x2 = 0 + -0.3333333333 5.25x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 5.25x + x2 = -0.3333333333 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = -0.3333333333 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = -0.3333333333 + 6.890625 Combine like terms: -0.3333333333 + 6.890625 = 6.5572916667 6.890625 + 5.25x + x2 = 6.5572916667 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 6.5572916667 Calculate the square root of the right side: 2.560720927 Break this problem into two subproblems by setting (x + 2.625) equal to 2.560720927 and -2.560720927.Subproblem 1
x + 2.625 = 2.560720927 Simplifying x + 2.625 = 2.560720927 Reorder the terms: 2.625 + x = 2.560720927 Solving 2.625 + x = 2.560720927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 2.560720927 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.560720927 + -2.625 x = 2.560720927 + -2.625 Combine like terms: 2.560720927 + -2.625 = -0.064279073 x = -0.064279073 Simplifying x = -0.064279073Subproblem 2
x + 2.625 = -2.560720927 Simplifying x + 2.625 = -2.560720927 Reorder the terms: 2.625 + x = -2.560720927 Solving 2.625 + x = -2.560720927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -2.560720927 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.560720927 + -2.625 x = -2.560720927 + -2.625 Combine like terms: -2.560720927 + -2.625 = -5.185720927 x = -5.185720927 Simplifying x = -5.185720927Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.064279073, -5.185720927}
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