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Simplifying x2 + 14x + -86 = -6 Reorder the terms: -86 + 14x + x2 = -6 Solving -86 + 14x + x2 = -6 Solving for variable 'x'. Reorder the terms: -86 + 6 + 14x + x2 = -6 + 6 Combine like terms: -86 + 6 = -80 -80 + 14x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -80 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 14x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 14x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 14x + x2 = 0 + 80 14x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 14x + x2 = 80 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 = 80 + 49 Reorder the terms: 49 + 14x + x2 = 80 + 49 Combine like terms: 80 + 49 = 129 49 + 14x + x2 = 129 Factor a perfect square on the left side: (x + 7)(x + 7) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + 7) equal to 11.357816692 and -11.357816692.Subproblem 1
x + 7 = 11.357816692 Simplifying x + 7 = 11.357816692 Reorder the terms: 7 + x = 11.357816692 Solving 7 + x = 11.357816692 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 = 11.357816692 + -7 Combine like terms: 7 + -7 = 0 0 + x = 11.357816692 + -7 x = 11.357816692 + -7 Combine like terms: 11.357816692 + -7 = 4.357816692 x = 4.357816692 Simplifying x = 4.357816692Subproblem 2
x + 7 = -11.357816692 Simplifying x + 7 = -11.357816692 Reorder the terms: 7 + x = -11.357816692 Solving 7 + x = -11.357816692 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 = -11.357816692 + -7 Combine like terms: 7 + -7 = 0 0 + x = -11.357816692 + -7 x = -11.357816692 + -7 Combine like terms: -11.357816692 + -7 = -18.357816692 x = -18.357816692 Simplifying x = -18.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.357816692, -18.357816692}
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