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Simplifying 0 = x2 + -36x + 32 Reorder the terms: 0 = 32 + -36x + x2 Solving 0 = 32 + -36x + x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + 36x + -1x2 = 32 + -36x + x2 + -32 + 36x + -1x2 Reorder the terms: -32 + 36x + -1x2 = 32 + -32 + -36x + 36x + x2 + -1x2 Combine like terms: 32 + -32 = 0 -32 + 36x + -1x2 = 0 + -36x + 36x + x2 + -1x2 -32 + 36x + -1x2 = -36x + 36x + x2 + -1x2 Combine like terms: -36x + 36x = 0 -32 + 36x + -1x2 = 0 + x2 + -1x2 -32 + 36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + 36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -36x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -36x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -36x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -36x + x2 = 0 + -32 -36x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -36x + x2 = -32 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 = -32 + 324 Reorder the terms: 324 + -36x + x2 = -32 + 324 Combine like terms: -32 + 324 = 292 324 + -36x + x2 = 292 Factor a perfect square on the left side: (x + -18)(x + -18) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + -18) equal to 17.088007491 and -17.088007491.Subproblem 1
x + -18 = 17.088007491 Simplifying x + -18 = 17.088007491 Reorder the terms: -18 + x = 17.088007491 Solving -18 + x = 17.088007491 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 = 17.088007491 + 18 Combine like terms: -18 + 18 = 0 0 + x = 17.088007491 + 18 x = 17.088007491 + 18 Combine like terms: 17.088007491 + 18 = 35.088007491 x = 35.088007491 Simplifying x = 35.088007491Subproblem 2
x + -18 = -17.088007491 Simplifying x + -18 = -17.088007491 Reorder the terms: -18 + x = -17.088007491 Solving -18 + x = -17.088007491 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 = -17.088007491 + 18 Combine like terms: -18 + 18 = 0 0 + x = -17.088007491 + 18 x = -17.088007491 + 18 Combine like terms: -17.088007491 + 18 = 0.911992509 x = 0.911992509 Simplifying x = 0.911992509Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.088007491, 0.911992509}
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