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Simplifying x2 + -14x + -127 = 0 Reorder the terms: -127 + -14x + x2 = 0 Solving -127 + -14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + -14x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + -14x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + -14x + x2 = 0 + 127 -14x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 -14x + x2 = 127 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 = 127 + 49 Reorder the terms: 49 + -14x + x2 = 127 + 49 Combine like terms: 127 + 49 = 176 49 + -14x + x2 = 176 Factor a perfect square on the left side: (x + -7)(x + -7) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + -7) equal to 13.266499161 and -13.266499161.Subproblem 1
x + -7 = 13.266499161 Simplifying x + -7 = 13.266499161 Reorder the terms: -7 + x = 13.266499161 Solving -7 + x = 13.266499161 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 = 13.266499161 + 7 Combine like terms: -7 + 7 = 0 0 + x = 13.266499161 + 7 x = 13.266499161 + 7 Combine like terms: 13.266499161 + 7 = 20.266499161 x = 20.266499161 Simplifying x = 20.266499161Subproblem 2
x + -7 = -13.266499161 Simplifying x + -7 = -13.266499161 Reorder the terms: -7 + x = -13.266499161 Solving -7 + x = -13.266499161 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 = -13.266499161 + 7 Combine like terms: -7 + 7 = 0 0 + x = -13.266499161 + 7 x = -13.266499161 + 7 Combine like terms: -13.266499161 + 7 = -6.266499161 x = -6.266499161 Simplifying x = -6.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.266499161, -6.266499161}
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