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Simplifying 180 = x2 + 22x Reorder the terms: 180 = 22x + x2 Solving 180 = 22x + x2 Solving for variable 'x'. Reorder the terms: 180 + -22x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 180 + -22x + -1x2 = 0 + x2 + -1x2 180 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + 22x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 22x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 22x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 22x + x2 = 0 + 180 22x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 22x + x2 = 180 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 180 + 121 Reorder the terms: 121 + 22x + x2 = 180 + 121 Combine like terms: 180 + 121 = 301 121 + 22x + x2 = 301 Factor a perfect square on the left side: (x + 11)(x + 11) = 301 Calculate the square root of the right side: 17.349351573 Break this problem into two subproblems by setting (x + 11) equal to 17.349351573 and -17.349351573.Subproblem 1
x + 11 = 17.349351573 Simplifying x + 11 = 17.349351573 Reorder the terms: 11 + x = 17.349351573 Solving 11 + x = 17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 17.349351573 + -11 Combine like terms: 11 + -11 = 0 0 + x = 17.349351573 + -11 x = 17.349351573 + -11 Combine like terms: 17.349351573 + -11 = 6.349351573 x = 6.349351573 Simplifying x = 6.349351573Subproblem 2
x + 11 = -17.349351573 Simplifying x + 11 = -17.349351573 Reorder the terms: 11 + x = -17.349351573 Solving 11 + x = -17.349351573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -17.349351573 + -11 Combine like terms: 11 + -11 = 0 0 + x = -17.349351573 + -11 x = -17.349351573 + -11 Combine like terms: -17.349351573 + -11 = -28.349351573 x = -28.349351573 Simplifying x = -28.349351573Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.349351573, -28.349351573}
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