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Simplifying x2 + -3.986x + 1.984 = 0 Reorder the terms: 1.984 + -3.986x + x2 = 0 Solving 1.984 + -3.986x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.984' to each side of the equation. 1.984 + -3.986x + -1.984 + x2 = 0 + -1.984 Reorder the terms: 1.984 + -1.984 + -3.986x + x2 = 0 + -1.984 Combine like terms: 1.984 + -1.984 = 0.000 0.000 + -3.986x + x2 = 0 + -1.984 -3.986x + x2 = 0 + -1.984 Combine like terms: 0 + -1.984 = -1.984 -3.986x + x2 = -1.984 The x term is -3.986x. Take half its coefficient (-1.993). Square it (3.972049) and add it to both sides. Add '3.972049' to each side of the equation. -3.986x + 3.972049 + x2 = -1.984 + 3.972049 Reorder the terms: 3.972049 + -3.986x + x2 = -1.984 + 3.972049 Combine like terms: -1.984 + 3.972049 = 1.988049 3.972049 + -3.986x + x2 = 1.988049 Factor a perfect square on the left side: (x + -1.993)(x + -1.993) = 1.988049 Calculate the square root of the right side: 1.409981915 Break this problem into two subproblems by setting (x + -1.993) equal to 1.409981915 and -1.409981915.Subproblem 1
x + -1.993 = 1.409981915 Simplifying x + -1.993 = 1.409981915 Reorder the terms: -1.993 + x = 1.409981915 Solving -1.993 + x = 1.409981915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.993' to each side of the equation. -1.993 + 1.993 + x = 1.409981915 + 1.993 Combine like terms: -1.993 + 1.993 = 0.000 0.000 + x = 1.409981915 + 1.993 x = 1.409981915 + 1.993 Combine like terms: 1.409981915 + 1.993 = 3.402981915 x = 3.402981915 Simplifying x = 3.402981915Subproblem 2
x + -1.993 = -1.409981915 Simplifying x + -1.993 = -1.409981915 Reorder the terms: -1.993 + x = -1.409981915 Solving -1.993 + x = -1.409981915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.993' to each side of the equation. -1.993 + 1.993 + x = -1.409981915 + 1.993 Combine like terms: -1.993 + 1.993 = 0.000 0.000 + x = -1.409981915 + 1.993 x = -1.409981915 + 1.993 Combine like terms: -1.409981915 + 1.993 = 0.583018085 x = 0.583018085 Simplifying x = 0.583018085Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.402981915, 0.583018085}
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