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Simplifying x2 + -6x + -96 = 0 Reorder the terms: -96 + -6x + x2 = 0 Solving -96 + -6x + x2 = 0 Solving for variable 'x'. 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 = 13.246950766 x = 13.246950766 Simplifying x = 13.246950766Subproblem 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 = -7.246950766 x = -7.246950766 Simplifying x = -7.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.246950766, -7.246950766}
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