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Simplifying x2 + -12x + 36 = 352 Reorder the terms: 36 + -12x + x2 = 352 Solving 36 + -12x + x2 = 352 Solving for variable 'x'. Reorder the terms: 36 + -352 + -12x + x2 = 352 + -352 Combine like terms: 36 + -352 = -316 -316 + -12x + x2 = 352 + -352 Combine like terms: 352 + -352 = 0 -316 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '316' to each side of the equation. -316 + -12x + 316 + x2 = 0 + 316 Reorder the terms: -316 + 316 + -12x + x2 = 0 + 316 Combine like terms: -316 + 316 = 0 0 + -12x + x2 = 0 + 316 -12x + x2 = 0 + 316 Combine like terms: 0 + 316 = 316 -12x + x2 = 316 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 = 316 + 36 Reorder the terms: 36 + -12x + x2 = 316 + 36 Combine like terms: 316 + 36 = 352 36 + -12x + x2 = 352 Factor a perfect square on the left side: (x + -6)(x + -6) = 352 Calculate the square root of the right side: 18.761663039 Break this problem into two subproblems by setting (x + -6) equal to 18.761663039 and -18.761663039.Subproblem 1
x + -6 = 18.761663039 Simplifying x + -6 = 18.761663039 Reorder the terms: -6 + x = 18.761663039 Solving -6 + x = 18.761663039 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 = 18.761663039 + 6 Combine like terms: -6 + 6 = 0 0 + x = 18.761663039 + 6 x = 18.761663039 + 6 Combine like terms: 18.761663039 + 6 = 24.761663039 x = 24.761663039 Simplifying x = 24.761663039Subproblem 2
x + -6 = -18.761663039 Simplifying x + -6 = -18.761663039 Reorder the terms: -6 + x = -18.761663039 Solving -6 + x = -18.761663039 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 = -18.761663039 + 6 Combine like terms: -6 + 6 = 0 0 + x = -18.761663039 + 6 x = -18.761663039 + 6 Combine like terms: -18.761663039 + 6 = -12.761663039 x = -12.761663039 Simplifying x = -12.761663039Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.761663039, -12.761663039}
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