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Simplifying x2 + -85x + 170 = 0 Reorder the terms: 170 + -85x + x2 = 0 Solving 170 + -85x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-170' to each side of the equation. 170 + -85x + -170 + x2 = 0 + -170 Reorder the terms: 170 + -170 + -85x + x2 = 0 + -170 Combine like terms: 170 + -170 = 0 0 + -85x + x2 = 0 + -170 -85x + x2 = 0 + -170 Combine like terms: 0 + -170 = -170 -85x + x2 = -170 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = -170 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = -170 + 1806.25 Combine like terms: -170 + 1806.25 = 1636.25 1806.25 + -85x + x2 = 1636.25 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 1636.25 Calculate the square root of the right side: 40.45058714 Break this problem into two subproblems by setting (x + -42.5) equal to 40.45058714 and -40.45058714.Subproblem 1
x + -42.5 = 40.45058714 Simplifying x + -42.5 = 40.45058714 Reorder the terms: -42.5 + x = 40.45058714 Solving -42.5 + x = 40.45058714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 40.45058714 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 40.45058714 + 42.5 x = 40.45058714 + 42.5 Combine like terms: 40.45058714 + 42.5 = 82.95058714 x = 82.95058714 Simplifying x = 82.95058714Subproblem 2
x + -42.5 = -40.45058714 Simplifying x + -42.5 = -40.45058714 Reorder the terms: -42.5 + x = -40.45058714 Solving -42.5 + x = -40.45058714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -40.45058714 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -40.45058714 + 42.5 x = -40.45058714 + 42.5 Combine like terms: -40.45058714 + 42.5 = 2.04941286 x = 2.04941286 Simplifying x = 2.04941286Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.95058714, 2.04941286}
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