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Simplifying x2 + 6x + -156 = 0 Reorder the terms: -156 + 6x + x2 = 0 Solving -156 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + 6x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + 6x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 6x + x2 = 0 + 156 6x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 6x + x2 = 156 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 = 156 + 9 Reorder the terms: 9 + 6x + x2 = 156 + 9 Combine like terms: 156 + 9 = 165 9 + 6x + x2 = 165 Factor a perfect square on the left side: (x + 3)(x + 3) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + 3) equal to 12.845232579 and -12.845232579.Subproblem 1
x + 3 = 12.845232579 Simplifying x + 3 = 12.845232579 Reorder the terms: 3 + x = 12.845232579 Solving 3 + x = 12.845232579 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 = 12.845232579 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.845232579 + -3 x = 12.845232579 + -3 Combine like terms: 12.845232579 + -3 = 9.845232579 x = 9.845232579 Simplifying x = 9.845232579Subproblem 2
x + 3 = -12.845232579 Simplifying x + 3 = -12.845232579 Reorder the terms: 3 + x = -12.845232579 Solving 3 + x = -12.845232579 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 = -12.845232579 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.845232579 + -3 x = -12.845232579 + -3 Combine like terms: -12.845232579 + -3 = -15.845232579 x = -15.845232579 Simplifying x = -15.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.845232579, -15.845232579}
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