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Simplifying x(x + 14) = 180 Reorder the terms: x(14 + x) = 180 (14 * x + x * x) = 180 (14x + x2) = 180 Solving 14x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 14x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 14x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 14x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 14x + x2 = 0 + 180 14x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 14x + x2 = 180 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 180 + 49 Reorder the terms: 49 + 14x + x2 = 180 + 49 Combine like terms: 180 + 49 = 229 49 + 14x + x2 = 229 Factor a perfect square on the left side: (x + 7)(x + 7) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (x + 7) equal to 15.13274595 and -15.13274595.Subproblem 1
x + 7 = 15.13274595 Simplifying x + 7 = 15.13274595 Reorder the terms: 7 + x = 15.13274595 Solving 7 + x = 15.13274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.13274595 + -7 x = 15.13274595 + -7 Combine like terms: 15.13274595 + -7 = 8.13274595 x = 8.13274595 Simplifying x = 8.13274595Subproblem 2
x + 7 = -15.13274595 Simplifying x + 7 = -15.13274595 Reorder the terms: 7 + x = -15.13274595 Solving 7 + x = -15.13274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.13274595 + -7 x = -15.13274595 + -7 Combine like terms: -15.13274595 + -7 = -22.13274595 x = -22.13274595 Simplifying x = -22.13274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.13274595, -22.13274595}
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