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Simplifying 0 = x2 + -36x + 100 Reorder the terms: 0 = 100 + -36x + x2 Solving 0 = 100 + -36x + x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + 36x + -1x2 = 100 + -36x + x2 + -100 + 36x + -1x2 Reorder the terms: -100 + 36x + -1x2 = 100 + -100 + -36x + 36x + x2 + -1x2 Combine like terms: 100 + -100 = 0 -100 + 36x + -1x2 = 0 + -36x + 36x + x2 + -1x2 -100 + 36x + -1x2 = -36x + 36x + x2 + -1x2 Combine like terms: -36x + 36x = 0 -100 + 36x + -1x2 = 0 + x2 + -1x2 -100 + 36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -100 + 36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -36x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -36x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -36x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -36x + x2 = 0 + -100 -36x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -36x + x2 = -100 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 = -100 + 324 Reorder the terms: 324 + -36x + x2 = -100 + 324 Combine like terms: -100 + 324 = 224 324 + -36x + x2 = 224 Factor a perfect square on the left side: (x + -18)(x + -18) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + -18) equal to 14.966629547 and -14.966629547.Subproblem 1
x + -18 = 14.966629547 Simplifying x + -18 = 14.966629547 Reorder the terms: -18 + x = 14.966629547 Solving -18 + x = 14.966629547 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 = 14.966629547 + 18 Combine like terms: -18 + 18 = 0 0 + x = 14.966629547 + 18 x = 14.966629547 + 18 Combine like terms: 14.966629547 + 18 = 32.966629547 x = 32.966629547 Simplifying x = 32.966629547Subproblem 2
x + -18 = -14.966629547 Simplifying x + -18 = -14.966629547 Reorder the terms: -18 + x = -14.966629547 Solving -18 + x = -14.966629547 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 = -14.966629547 + 18 Combine like terms: -18 + 18 = 0 0 + x = -14.966629547 + 18 x = -14.966629547 + 18 Combine like terms: -14.966629547 + 18 = 3.033370453 x = 3.033370453 Simplifying x = 3.033370453Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.966629547, 3.033370453}
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