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Simplifying 3x2 + -24x = 28 Reorder the terms: -24x + 3x2 = 28 Solving -24x + 3x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -24x + 3x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -8x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -8x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -8x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -8x + x2 = 0 + 9.333333333 -8x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -8x + x2 = 9.333333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 9.333333333 + 16 Reorder the terms: 16 + -8x + x2 = 9.333333333 + 16 Combine like terms: 9.333333333 + 16 = 25.333333333 16 + -8x + x2 = 25.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 25.333333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x + -4) equal to 5.033222957 and -5.033222957.Subproblem 1
x + -4 = 5.033222957 Simplifying x + -4 = 5.033222957 Reorder the terms: -4 + x = 5.033222957 Solving -4 + x = 5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.033222957 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.033222957 + 4 x = 5.033222957 + 4 Combine like terms: 5.033222957 + 4 = 9.033222957 x = 9.033222957 Simplifying x = 9.033222957Subproblem 2
x + -4 = -5.033222957 Simplifying x + -4 = -5.033222957 Reorder the terms: -4 + x = -5.033222957 Solving -4 + x = -5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.033222957 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.033222957 + 4 x = -5.033222957 + 4 Combine like terms: -5.033222957 + 4 = -1.033222957 x = -1.033222957 Simplifying x = -1.033222957Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.033222957, -1.033222957}
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