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Simplifying x2 + 14x + -79 = 0 Reorder the terms: -79 + 14x + x2 = 0 Solving -79 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + 14x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + 14x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + 14x + x2 = 0 + 79 14x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 14x + x2 = 79 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 = 79 + 49 Reorder the terms: 49 + 14x + x2 = 79 + 49 Combine like terms: 79 + 49 = 128 49 + 14x + x2 = 128 Factor a perfect square on the left side: (x + 7)(x + 7) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + 7) equal to 11.313708499 and -11.313708499.Subproblem 1
x + 7 = 11.313708499 Simplifying x + 7 = 11.313708499 Reorder the terms: 7 + x = 11.313708499 Solving 7 + x = 11.313708499 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 = 11.313708499 + -7 Combine like terms: 7 + -7 = 0 0 + x = 11.313708499 + -7 x = 11.313708499 + -7 Combine like terms: 11.313708499 + -7 = 4.313708499 x = 4.313708499 Simplifying x = 4.313708499Subproblem 2
x + 7 = -11.313708499 Simplifying x + 7 = -11.313708499 Reorder the terms: 7 + x = -11.313708499 Solving 7 + x = -11.313708499 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 = -11.313708499 + -7 Combine like terms: 7 + -7 = 0 0 + x = -11.313708499 + -7 x = -11.313708499 + -7 Combine like terms: -11.313708499 + -7 = -18.313708499 x = -18.313708499 Simplifying x = -18.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.313708499, -18.313708499}
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