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Simplifying x2 + -12x + -261 = 0 Reorder the terms: -261 + -12x + x2 = 0 Solving -261 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '261' to each side of the equation. -261 + -12x + 261 + x2 = 0 + 261 Reorder the terms: -261 + 261 + -12x + x2 = 0 + 261 Combine like terms: -261 + 261 = 0 0 + -12x + x2 = 0 + 261 -12x + x2 = 0 + 261 Combine like terms: 0 + 261 = 261 -12x + x2 = 261 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 = 261 + 36 Reorder the terms: 36 + -12x + x2 = 261 + 36 Combine like terms: 261 + 36 = 297 36 + -12x + x2 = 297 Factor a perfect square on the left side: (x + -6)(x + -6) = 297 Calculate the square root of the right side: 17.23368794 Break this problem into two subproblems by setting (x + -6) equal to 17.23368794 and -17.23368794.Subproblem 1
x + -6 = 17.23368794 Simplifying x + -6 = 17.23368794 Reorder the terms: -6 + x = 17.23368794 Solving -6 + x = 17.23368794 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 = 17.23368794 + 6 Combine like terms: -6 + 6 = 0 0 + x = 17.23368794 + 6 x = 17.23368794 + 6 Combine like terms: 17.23368794 + 6 = 23.23368794 x = 23.23368794 Simplifying x = 23.23368794Subproblem 2
x + -6 = -17.23368794 Simplifying x + -6 = -17.23368794 Reorder the terms: -6 + x = -17.23368794 Solving -6 + x = -17.23368794 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 = -17.23368794 + 6 Combine like terms: -6 + 6 = 0 0 + x = -17.23368794 + 6 x = -17.23368794 + 6 Combine like terms: -17.23368794 + 6 = -11.23368794 x = -11.23368794 Simplifying x = -11.23368794Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.23368794, -11.23368794}
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