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Simplifying x * x + 12x + -162 = 0 Multiply x * x x2 + 12x + -162 = 0 Reorder the terms: -162 + 12x + x2 = 0 Solving -162 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 12x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + 12x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 12x + x2 = 0 + 162 12x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 12x + x2 = 162 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 = 162 + 36 Reorder the terms: 36 + 12x + x2 = 162 + 36 Combine like terms: 162 + 36 = 198 36 + 12x + x2 = 198 Factor a perfect square on the left side: (x + 6)(x + 6) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (x + 6) equal to 14.071247279 and -14.071247279.Subproblem 1
x + 6 = 14.071247279 Simplifying x + 6 = 14.071247279 Reorder the terms: 6 + x = 14.071247279 Solving 6 + x = 14.071247279 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 = 14.071247279 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.071247279 + -6 x = 14.071247279 + -6 Combine like terms: 14.071247279 + -6 = 8.071247279 x = 8.071247279 Simplifying x = 8.071247279Subproblem 2
x + 6 = -14.071247279 Simplifying x + 6 = -14.071247279 Reorder the terms: 6 + x = -14.071247279 Solving 6 + x = -14.071247279 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 = -14.071247279 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.071247279 + -6 x = -14.071247279 + -6 Combine like terms: -14.071247279 + -6 = -20.071247279 x = -20.071247279 Simplifying x = -20.071247279Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.071247279, -20.071247279}
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