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Simplifying 36 = x2 + 36x Reorder the terms: 36 = 36x + x2 Solving 36 = 36x + x2 Solving for variable 'x'. Reorder the terms: 36 + -36x + -1x2 = 36x + -36x + x2 + -1x2 Combine like terms: 36x + -36x = 0 36 + -36x + -1x2 = 0 + x2 + -1x2 36 + -36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + -36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 36x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 36x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 36x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 36x + x2 = 0 + 36 36x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 36x + x2 = 36 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 = 36 + 324 Reorder the terms: 324 + 36x + x2 = 36 + 324 Combine like terms: 36 + 324 = 360 324 + 36x + x2 = 360 Factor a perfect square on the left side: (x + 18)(x + 18) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x + 18) equal to 18.973665961 and -18.973665961.Subproblem 1
x + 18 = 18.973665961 Simplifying x + 18 = 18.973665961 Reorder the terms: 18 + x = 18.973665961 Solving 18 + x = 18.973665961 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 = 18.973665961 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.973665961 + -18 x = 18.973665961 + -18 Combine like terms: 18.973665961 + -18 = 0.973665961 x = 0.973665961 Simplifying x = 0.973665961Subproblem 2
x + 18 = -18.973665961 Simplifying x + 18 = -18.973665961 Reorder the terms: 18 + x = -18.973665961 Solving 18 + x = -18.973665961 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 = -18.973665961 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.973665961 + -18 x = -18.973665961 + -18 Combine like terms: -18.973665961 + -18 = -36.973665961 x = -36.973665961 Simplifying x = -36.973665961Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.973665961, -36.973665961}
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