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Simplifying x2 + -8.5x + 2 = 0 Reorder the terms: 2 + -8.5x + x2 = 0 Solving 2 + -8.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -8.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -8.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -8.5x + x2 = 0 + -2 -8.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -8.5x + x2 = -2 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -2 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -2 + 18.0625 Combine like terms: -2 + 18.0625 = 16.0625 18.0625 + -8.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -4.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -4.25 = 4.007804885 Simplifying x + -4.25 = 4.007804885 Reorder the terms: -4.25 + x = 4.007804885 Solving -4.25 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.007804885 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.007804885 + 4.25 x = 4.007804885 + 4.25 Combine like terms: 4.007804885 + 4.25 = 8.257804885 x = 8.257804885 Simplifying x = 8.257804885Subproblem 2
x + -4.25 = -4.007804885 Simplifying x + -4.25 = -4.007804885 Reorder the terms: -4.25 + x = -4.007804885 Solving -4.25 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.007804885 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.007804885 + 4.25 x = -4.007804885 + 4.25 Combine like terms: -4.007804885 + 4.25 = 0.242195115 x = 0.242195115 Simplifying x = 0.242195115Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.257804885, 0.242195115}
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