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Simplifying x(x + 4) + (2x + -32) = 180 Reorder the terms: x(4 + x) + (2x + -32) = 180 (4 * x + x * x) + (2x + -32) = 180 (4x + x2) + (2x + -32) = 180 Reorder the terms: 4x + x2 + (-32 + 2x) = 180 Remove parenthesis around (-32 + 2x) 4x + x2 + -32 + 2x = 180 Reorder the terms: -32 + 4x + 2x + x2 = 180 Combine like terms: 4x + 2x = 6x -32 + 6x + x2 = 180 Solving -32 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: -32 + -180 + 6x + x2 = 180 + -180 Combine like terms: -32 + -180 = -212 -212 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -212 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '212' to each side of the equation. -212 + 6x + 212 + x2 = 0 + 212 Reorder the terms: -212 + 212 + 6x + x2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + 6x + x2 = 0 + 212 6x + x2 = 0 + 212 Combine like terms: 0 + 212 = 212 6x + x2 = 212 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 = 212 + 9 Reorder the terms: 9 + 6x + x2 = 212 + 9 Combine like terms: 212 + 9 = 221 9 + 6x + x2 = 221 Factor a perfect square on the left side: (x + 3)(x + 3) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + 3) equal to 14.866068747 and -14.866068747.Subproblem 1
x + 3 = 14.866068747 Simplifying x + 3 = 14.866068747 Reorder the terms: 3 + x = 14.866068747 Solving 3 + x = 14.866068747 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 = 14.866068747 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.866068747 + -3 x = 14.866068747 + -3 Combine like terms: 14.866068747 + -3 = 11.866068747 x = 11.866068747 Simplifying x = 11.866068747Subproblem 2
x + 3 = -14.866068747 Simplifying x + 3 = -14.866068747 Reorder the terms: 3 + x = -14.866068747 Solving 3 + x = -14.866068747 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 = -14.866068747 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.866068747 + -3 x = -14.866068747 + -3 Combine like terms: -14.866068747 + -3 = -17.866068747 x = -17.866068747 Simplifying x = -17.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.866068747, -17.866068747}
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