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Simplifying 14x = 18 + -1x2 Solving 14x = 18 + -1x2 Solving for variable 'x'. Reorder the terms: -18 + 14x + x2 = 18 + -1x2 + -18 + x2 Reorder the terms: -18 + 14x + x2 = 18 + -18 + -1x2 + x2 Combine like terms: 18 + -18 = 0 -18 + 14x + x2 = 0 + -1x2 + x2 -18 + 14x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -18 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 14x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 14x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 14x + x2 = 0 + 18 14x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 14x + x2 = 18 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 = 18 + 49 Reorder the terms: 49 + 14x + x2 = 18 + 49 Combine like terms: 18 + 49 = 67 49 + 14x + x2 = 67 Factor a perfect square on the left side: (x + 7)(x + 7) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 7) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 7 = 8.185352772 Simplifying x + 7 = 8.185352772 Reorder the terms: 7 + x = 8.185352772 Solving 7 + x = 8.185352772 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 = 8.185352772 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.185352772 + -7 x = 8.185352772 + -7 Combine like terms: 8.185352772 + -7 = 1.185352772 x = 1.185352772 Simplifying x = 1.185352772Subproblem 2
x + 7 = -8.185352772 Simplifying x + 7 = -8.185352772 Reorder the terms: 7 + x = -8.185352772 Solving 7 + x = -8.185352772 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 = -8.185352772 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.185352772 + -7 x = -8.185352772 + -7 Combine like terms: -8.185352772 + -7 = -15.185352772 x = -15.185352772 Simplifying x = -15.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.185352772, -15.185352772}
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