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Simplifying x2 + x = 274 Reorder the terms: x + x2 = 274 Solving x + x2 = 274 Solving for variable 'x'. Reorder the terms: -274 + x + x2 = 274 + -274 Combine like terms: 274 + -274 = 0 -274 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '274' to each side of the equation. -274 + x + 274 + x2 = 0 + 274 Reorder the terms: -274 + 274 + x + x2 = 0 + 274 Combine like terms: -274 + 274 = 0 0 + x + x2 = 0 + 274 x + x2 = 0 + 274 Combine like terms: 0 + 274 = 274 x + x2 = 274 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 = 274 + 0.25 Reorder the terms: 0.25 + x + x2 = 274 + 0.25 Combine like terms: 274 + 0.25 = 274.25 0.25 + x + x2 = 274.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 274.25 Calculate the square root of the right side: 16.560495162 Break this problem into two subproblems by setting (x + 0.5) equal to 16.560495162 and -16.560495162.Subproblem 1
x + 0.5 = 16.560495162 Simplifying x + 0.5 = 16.560495162 Reorder the terms: 0.5 + x = 16.560495162 Solving 0.5 + x = 16.560495162 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 = 16.560495162 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.560495162 + -0.5 x = 16.560495162 + -0.5 Combine like terms: 16.560495162 + -0.5 = 16.060495162 x = 16.060495162 Simplifying x = 16.060495162Subproblem 2
x + 0.5 = -16.560495162 Simplifying x + 0.5 = -16.560495162 Reorder the terms: 0.5 + x = -16.560495162 Solving 0.5 + x = -16.560495162 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 = -16.560495162 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.560495162 + -0.5 x = -16.560495162 + -0.5 Combine like terms: -16.560495162 + -0.5 = -17.060495162 x = -17.060495162 Simplifying x = -17.060495162Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.060495162, -17.060495162}
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