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Simplifying x2 + 12x = 257 Reorder the terms: 12x + x2 = 257 Solving 12x + x2 = 257 Solving for variable 'x'. Reorder the terms: -257 + 12x + x2 = 257 + -257 Combine like terms: 257 + -257 = 0 -257 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '257' to each side of the equation. -257 + 12x + 257 + x2 = 0 + 257 Reorder the terms: -257 + 257 + 12x + x2 = 0 + 257 Combine like terms: -257 + 257 = 0 0 + 12x + x2 = 0 + 257 12x + x2 = 0 + 257 Combine like terms: 0 + 257 = 257 12x + x2 = 257 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 = 257 + 36 Reorder the terms: 36 + 12x + x2 = 257 + 36 Combine like terms: 257 + 36 = 293 36 + 12x + x2 = 293 Factor a perfect square on the left side: (x + 6)(x + 6) = 293 Calculate the square root of the right side: 17.117242769 Break this problem into two subproblems by setting (x + 6) equal to 17.117242769 and -17.117242769.Subproblem 1
x + 6 = 17.117242769 Simplifying x + 6 = 17.117242769 Reorder the terms: 6 + x = 17.117242769 Solving 6 + x = 17.117242769 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 = 17.117242769 + -6 Combine like terms: 6 + -6 = 0 0 + x = 17.117242769 + -6 x = 17.117242769 + -6 Combine like terms: 17.117242769 + -6 = 11.117242769 x = 11.117242769 Simplifying x = 11.117242769Subproblem 2
x + 6 = -17.117242769 Simplifying x + 6 = -17.117242769 Reorder the terms: 6 + x = -17.117242769 Solving 6 + x = -17.117242769 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 = -17.117242769 + -6 Combine like terms: 6 + -6 = 0 0 + x = -17.117242769 + -6 x = -17.117242769 + -6 Combine like terms: -17.117242769 + -6 = -23.117242769 x = -23.117242769 Simplifying x = -23.117242769Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.117242769, -23.117242769}
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