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Simplifying x2 + 14x + -87 = -2 Reorder the terms: -87 + 14x + x2 = -2 Solving -87 + 14x + x2 = -2 Solving for variable 'x'. Reorder the terms: -87 + 2 + 14x + x2 = -2 + 2 Combine like terms: -87 + 2 = -85 -85 + 14x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -85 + 14x + x2 = 0 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 = 4.575836903 x = 4.575836903 Simplifying x = 4.575836903Subproblem 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 = -18.575836903 x = -18.575836903 Simplifying x = -18.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.575836903, -18.575836903}
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