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Simplifying 180 = (x2 + 5x) + x Reorder the terms: 180 = (5x + x2) + x Remove parenthesis around (5x + x2) 180 = 5x + x2 + x Reorder the terms: 180 = 5x + x + x2 Combine like terms: 5x + x = 6x 180 = 6x + x2 Solving 180 = 6x + x2 Solving for variable 'x'. Reorder the terms: 180 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 180 + -6x + -1x2 = 0 + x2 + -1x2 180 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + 6x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 6x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 6x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 6x + x2 = 0 + 180 6x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 6x + x2 = 180 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 180 + 9 Reorder the terms: 9 + 6x + x2 = 180 + 9 Combine like terms: 180 + 9 = 189 9 + 6x + x2 = 189 Factor a perfect square on the left side: (x + 3)(x + 3) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 3) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 3 = 13.747727085 Simplifying x + 3 = 13.747727085 Reorder the terms: 3 + x = 13.747727085 Solving 3 + x = 13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.747727085 + -3 x = 13.747727085 + -3 Combine like terms: 13.747727085 + -3 = 10.747727085 x = 10.747727085 Simplifying x = 10.747727085Subproblem 2
x + 3 = -13.747727085 Simplifying x + 3 = -13.747727085 Reorder the terms: 3 + x = -13.747727085 Solving 3 + x = -13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.747727085 + -3 x = -13.747727085 + -3 Combine like terms: -13.747727085 + -3 = -16.747727085 x = -16.747727085 Simplifying x = -16.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.747727085, -16.747727085}
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