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Simplifying x2 + -12x + -156 = 0 Reorder the terms: -156 + -12x + x2 = 0 Solving -156 + -12x + 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 + -12x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + -12x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -12x + x2 = 0 + 156 -12x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 -12x + x2 = 156 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 = 156 + 36 Reorder the terms: 36 + -12x + x2 = 156 + 36 Combine like terms: 156 + 36 = 192 36 + -12x + x2 = 192 Factor a perfect square on the left side: (x + -6)(x + -6) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + -6) equal to 13.856406461 and -13.856406461.Subproblem 1
x + -6 = 13.856406461 Simplifying x + -6 = 13.856406461 Reorder the terms: -6 + x = 13.856406461 Solving -6 + x = 13.856406461 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 = 13.856406461 + 6 Combine like terms: -6 + 6 = 0 0 + x = 13.856406461 + 6 x = 13.856406461 + 6 Combine like terms: 13.856406461 + 6 = 19.856406461 x = 19.856406461 Simplifying x = 19.856406461Subproblem 2
x + -6 = -13.856406461 Simplifying x + -6 = -13.856406461 Reorder the terms: -6 + x = -13.856406461 Solving -6 + x = -13.856406461 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 = -13.856406461 + 6 Combine like terms: -6 + 6 = 0 0 + x = -13.856406461 + 6 x = -13.856406461 + 6 Combine like terms: -13.856406461 + 6 = -7.856406461 x = -7.856406461 Simplifying x = -7.856406461Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.856406461, -7.856406461}
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