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Simplifying x2 + 14x = -10 Reorder the terms: 14x + x2 = -10 Solving 14x + x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + 14x + x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 14x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 14x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 14x + x2 = 0 + -10 14x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 14x + x2 = -10 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 = -10 + 49 Reorder the terms: 49 + 14x + x2 = -10 + 49 Combine like terms: -10 + 49 = 39 49 + 14x + x2 = 39 Factor a perfect square on the left side: (x + 7)(x + 7) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 7) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 7 = 6.244997998 Simplifying x + 7 = 6.244997998 Reorder the terms: 7 + x = 6.244997998 Solving 7 + x = 6.244997998 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 = 6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.244997998 + -7 x = 6.244997998 + -7 Combine like terms: 6.244997998 + -7 = -0.755002002 x = -0.755002002 Simplifying x = -0.755002002Subproblem 2
x + 7 = -6.244997998 Simplifying x + 7 = -6.244997998 Reorder the terms: 7 + x = -6.244997998 Solving 7 + x = -6.244997998 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 = -6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.244997998 + -7 x = -6.244997998 + -7 Combine like terms: -6.244997998 + -7 = -13.244997998 x = -13.244997998 Simplifying x = -13.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.755002002, -13.244997998}
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