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Simplifying x2 + 14x + 47 = 0 Reorder the terms: 47 + 14x + x2 = 0 Solving 47 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 14x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 14x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 14x + x2 = 0 + -47 14x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 14x + x2 = -47 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 = -47 + 49 Reorder the terms: 49 + 14x + x2 = -47 + 49 Combine like terms: -47 + 49 = 2 49 + 14x + x2 = 2 Factor a perfect square on the left side: (x + 7)(x + 7) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 7) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 7 = 1.414213562 Simplifying x + 7 = 1.414213562 Reorder the terms: 7 + x = 1.414213562 Solving 7 + x = 1.414213562 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 = 1.414213562 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.414213562 + -7 x = 1.414213562 + -7 Combine like terms: 1.414213562 + -7 = -5.585786438 x = -5.585786438 Simplifying x = -5.585786438Subproblem 2
x + 7 = -1.414213562 Simplifying x + 7 = -1.414213562 Reorder the terms: 7 + x = -1.414213562 Solving 7 + x = -1.414213562 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 = -1.414213562 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.414213562 + -7 x = -1.414213562 + -7 Combine like terms: -1.414213562 + -7 = -8.414213562 x = -8.414213562 Simplifying x = -8.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.585786438, -8.414213562}
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