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Simplifying 3x2 + 12x + -64 = 0 Reorder the terms: -64 + 12x + 3x2 = 0 Solving -64 + 12x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + 4x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + 4x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + 4x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 21.33333333 4x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 4x + x2 = 21.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 21.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 21.33333333 + 4 Combine like terms: 21.33333333 + 4 = 25.33333333 4 + 4x + x2 = 25.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 25.33333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x + 2) equal to 5.033222957 and -5.033222957.Subproblem 1
x + 2 = 5.033222957 Simplifying x + 2 = 5.033222957 Reorder the terms: 2 + x = 5.033222957 Solving 2 + x = 5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.033222957 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.033222957 + -2 x = 5.033222957 + -2 Combine like terms: 5.033222957 + -2 = 3.033222957 x = 3.033222957 Simplifying x = 3.033222957Subproblem 2
x + 2 = -5.033222957 Simplifying x + 2 = -5.033222957 Reorder the terms: 2 + x = -5.033222957 Solving 2 + x = -5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.033222957 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.033222957 + -2 x = -5.033222957 + -2 Combine like terms: -5.033222957 + -2 = -7.033222957 x = -7.033222957 Simplifying x = -7.033222957Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.033222957, -7.033222957}
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