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Simplifying x2 + -12x + -365 = 0 Reorder the terms: -365 + -12x + x2 = 0 Solving -365 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '365' to each side of the equation. -365 + -12x + 365 + x2 = 0 + 365 Reorder the terms: -365 + 365 + -12x + x2 = 0 + 365 Combine like terms: -365 + 365 = 0 0 + -12x + x2 = 0 + 365 -12x + x2 = 0 + 365 Combine like terms: 0 + 365 = 365 -12x + x2 = 365 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 = 365 + 36 Reorder the terms: 36 + -12x + x2 = 365 + 36 Combine like terms: 365 + 36 = 401 36 + -12x + x2 = 401 Factor a perfect square on the left side: (x + -6)(x + -6) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + -6) equal to 20.024984395 and -20.024984395.Subproblem 1
x + -6 = 20.024984395 Simplifying x + -6 = 20.024984395 Reorder the terms: -6 + x = 20.024984395 Solving -6 + x = 20.024984395 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 = 20.024984395 + 6 Combine like terms: -6 + 6 = 0 0 + x = 20.024984395 + 6 x = 20.024984395 + 6 Combine like terms: 20.024984395 + 6 = 26.024984395 x = 26.024984395 Simplifying x = 26.024984395Subproblem 2
x + -6 = -20.024984395 Simplifying x + -6 = -20.024984395 Reorder the terms: -6 + x = -20.024984395 Solving -6 + x = -20.024984395 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 = -20.024984395 + 6 Combine like terms: -6 + 6 = 0 0 + x = -20.024984395 + 6 x = -20.024984395 + 6 Combine like terms: -20.024984395 + 6 = -14.024984395 x = -14.024984395 Simplifying x = -14.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.024984395, -14.024984395}
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