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Simplifying -96 = -1x2 + 12x + 128 Reorder the terms: -96 = 128 + 12x + -1x2 Solving -96 = 128 + 12x + -1x2 Solving for variable 'x'. Combine like terms: -96 + -128 = -224 -224 + -12x + x2 = 128 + 12x + -1x2 + -128 + -12x + x2 Reorder the terms: -224 + -12x + x2 = 128 + -128 + 12x + -12x + -1x2 + x2 Combine like terms: 128 + -128 = 0 -224 + -12x + x2 = 0 + 12x + -12x + -1x2 + x2 -224 + -12x + x2 = 12x + -12x + -1x2 + x2 Combine like terms: 12x + -12x = 0 -224 + -12x + x2 = 0 + -1x2 + x2 -224 + -12x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -224 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + -12x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + -12x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + -12x + x2 = 0 + 224 -12x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 -12x + x2 = 224 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 224 + 36 Reorder the terms: 36 + -12x + x2 = 224 + 36 Combine like terms: 224 + 36 = 260 36 + -12x + x2 = 260 Factor a perfect square on the left side: (x + -6)(x + -6) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + -6) equal to 16.124515497 and -16.124515497.Subproblem 1
x + -6 = 16.124515497 Simplifying x + -6 = 16.124515497 Reorder the terms: -6 + x = 16.124515497 Solving -6 + x = 16.124515497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 16.124515497 + 6 Combine like terms: -6 + 6 = 0 0 + x = 16.124515497 + 6 x = 16.124515497 + 6 Combine like terms: 16.124515497 + 6 = 22.124515497 x = 22.124515497 Simplifying x = 22.124515497Subproblem 2
x + -6 = -16.124515497 Simplifying x + -6 = -16.124515497 Reorder the terms: -6 + x = -16.124515497 Solving -6 + x = -16.124515497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -16.124515497 + 6 Combine like terms: -6 + 6 = 0 0 + x = -16.124515497 + 6 x = -16.124515497 + 6 Combine like terms: -16.124515497 + 6 = -10.124515497 x = -10.124515497 Simplifying x = -10.124515497Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.124515497, -10.124515497}
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