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Simplifying x2 + -14x + -85 = 0 Reorder the terms: -85 + -14x + x2 = 0 Solving -85 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -14x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + -14x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -14x + x2 = 0 + 85 -14x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 -14x + x2 = 85 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 85 + 49 Reorder the terms: 49 + -14x + x2 = 85 + 49 Combine like terms: 85 + 49 = 134 49 + -14x + x2 = 134 Factor a perfect square on the left side: (x + -7)(x + -7) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + -7) equal to 11.575836903 and -11.575836903.Subproblem 1
x + -7 = 11.575836903 Simplifying x + -7 = 11.575836903 Reorder the terms: -7 + x = 11.575836903 Solving -7 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 11.575836903 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.575836903 + 7 x = 11.575836903 + 7 Combine like terms: 11.575836903 + 7 = 18.575836903 x = 18.575836903 Simplifying x = 18.575836903Subproblem 2
x + -7 = -11.575836903 Simplifying x + -7 = -11.575836903 Reorder the terms: -7 + x = -11.575836903 Solving -7 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -11.575836903 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.575836903 + 7 x = -11.575836903 + 7 Combine like terms: -11.575836903 + 7 = -4.575836903 x = -4.575836903 Simplifying x = -4.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.575836903, -4.575836903}
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