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Simplifying x2 + -36x + 45 = 5 Reorder the terms: 45 + -36x + x2 = 5 Solving 45 + -36x + x2 = 5 Solving for variable 'x'. Reorder the terms: 45 + -5 + -36x + x2 = 5 + -5 Combine like terms: 45 + -5 = 40 40 + -36x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 40 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -36x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -36x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -36x + x2 = 0 + -40 -36x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -36x + x2 = -40 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -40 + 324 Reorder the terms: 324 + -36x + x2 = -40 + 324 Combine like terms: -40 + 324 = 284 324 + -36x + x2 = 284 Factor a perfect square on the left side: (x + -18)(x + -18) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (x + -18) equal to 16.852299546 and -16.852299546.Subproblem 1
x + -18 = 16.852299546 Simplifying x + -18 = 16.852299546 Reorder the terms: -18 + x = 16.852299546 Solving -18 + x = 16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 16.852299546 + 18 Combine like terms: -18 + 18 = 0 0 + x = 16.852299546 + 18 x = 16.852299546 + 18 Combine like terms: 16.852299546 + 18 = 34.852299546 x = 34.852299546 Simplifying x = 34.852299546Subproblem 2
x + -18 = -16.852299546 Simplifying x + -18 = -16.852299546 Reorder the terms: -18 + x = -16.852299546 Solving -18 + x = -16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -16.852299546 + 18 Combine like terms: -18 + 18 = 0 0 + x = -16.852299546 + 18 x = -16.852299546 + 18 Combine like terms: -16.852299546 + 18 = 1.147700454 x = 1.147700454 Simplifying x = 1.147700454Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.852299546, 1.147700454}
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