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Simplifying x2 + 14x + -112 = 0 Reorder the terms: -112 + 14x + x2 = 0 Solving -112 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 14x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 14x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 14x + x2 = 0 + 112 14x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 14x + x2 = 112 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 = 112 + 49 Reorder the terms: 49 + 14x + x2 = 112 + 49 Combine like terms: 112 + 49 = 161 49 + 14x + x2 = 161 Factor a perfect square on the left side: (x + 7)(x + 7) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + 7) equal to 12.68857754 and -12.68857754.Subproblem 1
x + 7 = 12.68857754 Simplifying x + 7 = 12.68857754 Reorder the terms: 7 + x = 12.68857754 Solving 7 + x = 12.68857754 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 = 12.68857754 + -7 Combine like terms: 7 + -7 = 0 0 + x = 12.68857754 + -7 x = 12.68857754 + -7 Combine like terms: 12.68857754 + -7 = 5.68857754 x = 5.68857754 Simplifying x = 5.68857754Subproblem 2
x + 7 = -12.68857754 Simplifying x + 7 = -12.68857754 Reorder the terms: 7 + x = -12.68857754 Solving 7 + x = -12.68857754 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 = -12.68857754 + -7 Combine like terms: 7 + -7 = 0 0 + x = -12.68857754 + -7 x = -12.68857754 + -7 Combine like terms: -12.68857754 + -7 = -19.68857754 x = -19.68857754 Simplifying x = -19.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.68857754, -19.68857754}
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