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Simplifying x2 + -6x + -99 = 0 Reorder the terms: -99 + -6x + x2 = 0 Solving -99 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -6x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -6x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -6x + x2 = 0 + 99 -6x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -6x + x2 = 99 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 = 99 + 9 Reorder the terms: 9 + -6x + x2 = 99 + 9 Combine like terms: 99 + 9 = 108 9 + -6x + x2 = 108 Factor a perfect square on the left side: (x + -3)(x + -3) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -3) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -3 = 10.392304845 Simplifying x + -3 = 10.392304845 Reorder the terms: -3 + x = 10.392304845 Solving -3 + x = 10.392304845 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 = 10.392304845 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.392304845 + 3 x = 10.392304845 + 3 Combine like terms: 10.392304845 + 3 = 13.392304845 x = 13.392304845 Simplifying x = 13.392304845Subproblem 2
x + -3 = -10.392304845 Simplifying x + -3 = -10.392304845 Reorder the terms: -3 + x = -10.392304845 Solving -3 + x = -10.392304845 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 = -10.392304845 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.392304845 + 3 x = -10.392304845 + 3 Combine like terms: -10.392304845 + 3 = -7.392304845 x = -7.392304845 Simplifying x = -7.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.392304845, -7.392304845}
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