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Simplifying x2 + 6x = 96 Reorder the terms: 6x + x2 = 96 Solving 6x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 6x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 6x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 6x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 6x + x2 = 0 + 96 6x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 6x + x2 = 96 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 96 + 9 Reorder the terms: 9 + 6x + x2 = 96 + 9 Combine like terms: 96 + 9 = 105 9 + 6x + x2 = 105 Factor a perfect square on the left side: (x + 3)(x + 3) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 3) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 3 = 10.246950766 Simplifying x + 3 = 10.246950766 Reorder the terms: 3 + x = 10.246950766 Solving 3 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.246950766 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.246950766 + -3 x = 10.246950766 + -3 Combine like terms: 10.246950766 + -3 = 7.246950766 x = 7.246950766 Simplifying x = 7.246950766Subproblem 2
x + 3 = -10.246950766 Simplifying x + 3 = -10.246950766 Reorder the terms: 3 + x = -10.246950766 Solving 3 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.246950766 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.246950766 + -3 x = -10.246950766 + -3 Combine like terms: -10.246950766 + -3 = -13.246950766 x = -13.246950766 Simplifying x = -13.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.246950766, -13.246950766}
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