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Simplifying x2 + 14x = -20 Reorder the terms: 14x + x2 = -20 Solving 14x + x2 = -20 Solving for variable 'x'. Reorder the terms: 20 + 14x + x2 = -20 + 20 Combine like terms: -20 + 20 = 0 20 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 14x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 14x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 14x + x2 = 0 + -20 14x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 14x + x2 = -20 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 = -20 + 49 Reorder the terms: 49 + 14x + x2 = -20 + 49 Combine like terms: -20 + 49 = 29 49 + 14x + x2 = 29 Factor a perfect square on the left side: (x + 7)(x + 7) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 7) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 7 = 5.385164807 Simplifying x + 7 = 5.385164807 Reorder the terms: 7 + x = 5.385164807 Solving 7 + x = 5.385164807 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 = 5.385164807 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.385164807 + -7 x = 5.385164807 + -7 Combine like terms: 5.385164807 + -7 = -1.614835193 x = -1.614835193 Simplifying x = -1.614835193Subproblem 2
x + 7 = -5.385164807 Simplifying x + 7 = -5.385164807 Reorder the terms: 7 + x = -5.385164807 Solving 7 + x = -5.385164807 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 = -5.385164807 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.385164807 + -7 x = -5.385164807 + -7 Combine like terms: -5.385164807 + -7 = -12.385164807 x = -12.385164807 Simplifying x = -12.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.614835193, -12.385164807}
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