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Simplifying x2 + 12x = 331 Reorder the terms: 12x + x2 = 331 Solving 12x + x2 = 331 Solving for variable 'x'. Reorder the terms: -331 + 12x + x2 = 331 + -331 Combine like terms: 331 + -331 = 0 -331 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '331' to each side of the equation. -331 + 12x + 331 + x2 = 0 + 331 Reorder the terms: -331 + 331 + 12x + x2 = 0 + 331 Combine like terms: -331 + 331 = 0 0 + 12x + x2 = 0 + 331 12x + x2 = 0 + 331 Combine like terms: 0 + 331 = 331 12x + x2 = 331 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 = 331 + 36 Reorder the terms: 36 + 12x + x2 = 331 + 36 Combine like terms: 331 + 36 = 367 36 + 12x + x2 = 367 Factor a perfect square on the left side: (x + 6)(x + 6) = 367 Calculate the square root of the right side: 19.157244061 Break this problem into two subproblems by setting (x + 6) equal to 19.157244061 and -19.157244061.Subproblem 1
x + 6 = 19.157244061 Simplifying x + 6 = 19.157244061 Reorder the terms: 6 + x = 19.157244061 Solving 6 + x = 19.157244061 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 = 19.157244061 + -6 Combine like terms: 6 + -6 = 0 0 + x = 19.157244061 + -6 x = 19.157244061 + -6 Combine like terms: 19.157244061 + -6 = 13.157244061 x = 13.157244061 Simplifying x = 13.157244061Subproblem 2
x + 6 = -19.157244061 Simplifying x + 6 = -19.157244061 Reorder the terms: 6 + x = -19.157244061 Solving 6 + x = -19.157244061 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 = -19.157244061 + -6 Combine like terms: 6 + -6 = 0 0 + x = -19.157244061 + -6 x = -19.157244061 + -6 Combine like terms: -19.157244061 + -6 = -25.157244061 x = -25.157244061 Simplifying x = -25.157244061Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.157244061, -25.157244061}
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