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Simplifying x2 + x + -27.28171817 = 0 Reorder the terms: -27.28171817 + x + x2 = 0 Solving -27.28171817 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27.28171817' to each side of the equation. -27.28171817 + x + 27.28171817 + x2 = 0 + 27.28171817 Reorder the terms: -27.28171817 + 27.28171817 + x + x2 = 0 + 27.28171817 Combine like terms: -27.28171817 + 27.28171817 = 0.00000000 0.00000000 + x + x2 = 0 + 27.28171817 x + x2 = 0 + 27.28171817 Combine like terms: 0 + 27.28171817 = 27.28171817 x + x2 = 27.28171817 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 = 27.28171817 + 0.25 Reorder the terms: 0.25 + x + x2 = 27.28171817 + 0.25 Combine like terms: 27.28171817 + 0.25 = 27.53171817 0.25 + x + x2 = 27.53171817 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 27.53171817 Calculate the square root of the right side: 5.247067578 Break this problem into two subproblems by setting (x + 0.5) equal to 5.247067578 and -5.247067578.Subproblem 1
x + 0.5 = 5.247067578 Simplifying x + 0.5 = 5.247067578 Reorder the terms: 0.5 + x = 5.247067578 Solving 0.5 + x = 5.247067578 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 = 5.247067578 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.247067578 + -0.5 x = 5.247067578 + -0.5 Combine like terms: 5.247067578 + -0.5 = 4.747067578 x = 4.747067578 Simplifying x = 4.747067578Subproblem 2
x + 0.5 = -5.247067578 Simplifying x + 0.5 = -5.247067578 Reorder the terms: 0.5 + x = -5.247067578 Solving 0.5 + x = -5.247067578 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 = -5.247067578 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.247067578 + -0.5 x = -5.247067578 + -0.5 Combine like terms: -5.247067578 + -0.5 = -5.747067578 x = -5.747067578 Simplifying x = -5.747067578Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.747067578, -5.747067578}
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