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Simplifying x2 + x + 34 = 180 Reorder the terms: 34 + x + x2 = 180 Solving 34 + x + x2 = 180 Solving for variable 'x'. Reorder the terms: 34 + -180 + x + x2 = 180 + -180 Combine like terms: 34 + -180 = -146 -146 + x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -146 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + x + x2 = 0 + 146 x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 x + x2 = 146 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 146 + 0.25 Reorder the terms: 0.25 + x + x2 = 146 + 0.25 Combine like terms: 146 + 0.25 = 146.25 0.25 + x + x2 = 146.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + 0.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + 0.5 = 12.093386622 Simplifying x + 0.5 = 12.093386622 Reorder the terms: 0.5 + x = 12.093386622 Solving 0.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.093386622 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.093386622 + -0.5 x = 12.093386622 + -0.5 Combine like terms: 12.093386622 + -0.5 = 11.593386622 x = 11.593386622 Simplifying x = 11.593386622Subproblem 2
x + 0.5 = -12.093386622 Simplifying x + 0.5 = -12.093386622 Reorder the terms: 0.5 + x = -12.093386622 Solving 0.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.093386622 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.093386622 + -0.5 x = -12.093386622 + -0.5 Combine like terms: -12.093386622 + -0.5 = -12.593386622 x = -12.593386622 Simplifying x = -12.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.593386622, -12.593386622}
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