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Simplifying x2 + 36x = 492 Reorder the terms: 36x + x2 = 492 Solving 36x + x2 = 492 Solving for variable 'x'. Reorder the terms: -492 + 36x + x2 = 492 + -492 Combine like terms: 492 + -492 = 0 -492 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '492' to each side of the equation. -492 + 36x + 492 + x2 = 0 + 492 Reorder the terms: -492 + 492 + 36x + x2 = 0 + 492 Combine like terms: -492 + 492 = 0 0 + 36x + x2 = 0 + 492 36x + x2 = 0 + 492 Combine like terms: 0 + 492 = 492 36x + x2 = 492 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 = 492 + 324 Reorder the terms: 324 + 36x + x2 = 492 + 324 Combine like terms: 492 + 324 = 816 324 + 36x + x2 = 816 Factor a perfect square on the left side: (x + 18)(x + 18) = 816 Calculate the square root of the right side: 28.565713714 Break this problem into two subproblems by setting (x + 18) equal to 28.565713714 and -28.565713714.Subproblem 1
x + 18 = 28.565713714 Simplifying x + 18 = 28.565713714 Reorder the terms: 18 + x = 28.565713714 Solving 18 + x = 28.565713714 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 = 28.565713714 + -18 Combine like terms: 18 + -18 = 0 0 + x = 28.565713714 + -18 x = 28.565713714 + -18 Combine like terms: 28.565713714 + -18 = 10.565713714 x = 10.565713714 Simplifying x = 10.565713714Subproblem 2
x + 18 = -28.565713714 Simplifying x + 18 = -28.565713714 Reorder the terms: 18 + x = -28.565713714 Solving 18 + x = -28.565713714 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 = -28.565713714 + -18 Combine like terms: 18 + -18 = 0 0 + x = -28.565713714 + -18 x = -28.565713714 + -18 Combine like terms: -28.565713714 + -18 = -46.565713714 x = -46.565713714 Simplifying x = -46.565713714Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.565713714, -46.565713714}
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