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Simplifying x2 + 14x = -9 Reorder the terms: 14x + x2 = -9 Solving 14x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 14x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 14x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 14x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 14x + x2 = 0 + -9 14x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 14x + x2 = -9 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 = -9 + 49 Reorder the terms: 49 + 14x + x2 = -9 + 49 Combine like terms: -9 + 49 = 40 49 + 14x + x2 = 40 Factor a perfect square on the left side: (x + 7)(x + 7) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 7) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 7 = 6.32455532 Simplifying x + 7 = 6.32455532 Reorder the terms: 7 + x = 6.32455532 Solving 7 + x = 6.32455532 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 = 6.32455532 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.32455532 + -7 x = 6.32455532 + -7 Combine like terms: 6.32455532 + -7 = -0.67544468 x = -0.67544468 Simplifying x = -0.67544468Subproblem 2
x + 7 = -6.32455532 Simplifying x + 7 = -6.32455532 Reorder the terms: 7 + x = -6.32455532 Solving 7 + x = -6.32455532 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 = -6.32455532 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.32455532 + -7 x = -6.32455532 + -7 Combine like terms: -6.32455532 + -7 = -13.32455532 x = -13.32455532 Simplifying x = -13.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.67544468, -13.32455532}
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