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Simplifying x2 + 14x + 22 = 0 Reorder the terms: 22 + 14x + x2 = 0 Solving 22 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 14x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 14x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 14x + x2 = 0 + -22 14x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 14x + x2 = -22 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 = -22 + 49 Reorder the terms: 49 + 14x + x2 = -22 + 49 Combine like terms: -22 + 49 = 27 49 + 14x + x2 = 27 Factor a perfect square on the left side: (x + 7)(x + 7) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 7) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 7 = 5.196152423 Simplifying x + 7 = 5.196152423 Reorder the terms: 7 + x = 5.196152423 Solving 7 + x = 5.196152423 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 = 5.196152423 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.196152423 + -7 x = 5.196152423 + -7 Combine like terms: 5.196152423 + -7 = -1.803847577 x = -1.803847577 Simplifying x = -1.803847577Subproblem 2
x + 7 = -5.196152423 Simplifying x + 7 = -5.196152423 Reorder the terms: 7 + x = -5.196152423 Solving 7 + x = -5.196152423 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 = -5.196152423 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.196152423 + -7 x = -5.196152423 + -7 Combine like terms: -5.196152423 + -7 = -12.196152423 x = -12.196152423 Simplifying x = -12.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.803847577, -12.196152423}
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