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Simplifying x2 + 14x + 34 = 0 Reorder the terms: 34 + 14x + x2 = 0 Solving 34 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 14x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 14x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 14x + x2 = 0 + -34 14x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 14x + x2 = -34 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 = -34 + 49 Reorder the terms: 49 + 14x + x2 = -34 + 49 Combine like terms: -34 + 49 = 15 49 + 14x + x2 = 15 Factor a perfect square on the left side: (x + 7)(x + 7) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 7) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 7 = 3.872983346 Simplifying x + 7 = 3.872983346 Reorder the terms: 7 + x = 3.872983346 Solving 7 + x = 3.872983346 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 = 3.872983346 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.872983346 + -7 x = 3.872983346 + -7 Combine like terms: 3.872983346 + -7 = -3.127016654 x = -3.127016654 Simplifying x = -3.127016654Subproblem 2
x + 7 = -3.872983346 Simplifying x + 7 = -3.872983346 Reorder the terms: 7 + x = -3.872983346 Solving 7 + x = -3.872983346 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 = -3.872983346 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.872983346 + -7 x = -3.872983346 + -7 Combine like terms: -3.872983346 + -7 = -10.872983346 x = -10.872983346 Simplifying x = -10.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.127016654, -10.872983346}
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