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Simplifying 3x2 + 44x = 96 Reorder the terms: 44x + 3x2 = 96 Solving 44x + 3x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 44x + 3x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 44x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -32 + 14.66666667x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 14.66666667x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 14.66666667x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 14.66666667x + x2 = 0 + 32 14.66666667x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 14.66666667x + x2 = 32 The x term is 14.66666667x. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667x + 53.77777780 + x2 = 32 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667x + x2 = 32 + 53.77777780 Combine like terms: 32 + 53.77777780 = 85.7777778 53.77777780 + 14.66666667x + x2 = 85.7777778 Factor a perfect square on the left side: (x + 7.333333335)(x + 7.333333335) = 85.7777778 Calculate the square root of the right side: 9.261629328 Break this problem into two subproblems by setting (x + 7.333333335) equal to 9.261629328 and -9.261629328.Subproblem 1
x + 7.333333335 = 9.261629328 Simplifying x + 7.333333335 = 9.261629328 Reorder the terms: 7.333333335 + x = 9.261629328 Solving 7.333333335 + x = 9.261629328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = 9.261629328 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = 9.261629328 + -7.333333335 x = 9.261629328 + -7.333333335 Combine like terms: 9.261629328 + -7.333333335 = 1.928295993 x = 1.928295993 Simplifying x = 1.928295993Subproblem 2
x + 7.333333335 = -9.261629328 Simplifying x + 7.333333335 = -9.261629328 Reorder the terms: 7.333333335 + x = -9.261629328 Solving 7.333333335 + x = -9.261629328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = -9.261629328 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = -9.261629328 + -7.333333335 x = -9.261629328 + -7.333333335 Combine like terms: -9.261629328 + -7.333333335 = -16.594962663 x = -16.594962663 Simplifying x = -16.594962663Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.928295993, -16.594962663}
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