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Simplifying x2 + 6x = 388 Reorder the terms: 6x + x2 = 388 Solving 6x + x2 = 388 Solving for variable 'x'. Reorder the terms: -388 + 6x + x2 = 388 + -388 Combine like terms: 388 + -388 = 0 -388 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '388' to each side of the equation. -388 + 6x + 388 + x2 = 0 + 388 Reorder the terms: -388 + 388 + 6x + x2 = 0 + 388 Combine like terms: -388 + 388 = 0 0 + 6x + x2 = 0 + 388 6x + x2 = 0 + 388 Combine like terms: 0 + 388 = 388 6x + x2 = 388 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 388 + 9 Reorder the terms: 9 + 6x + x2 = 388 + 9 Combine like terms: 388 + 9 = 397 9 + 6x + x2 = 397 Factor a perfect square on the left side: (x + 3)(x + 3) = 397 Calculate the square root of the right side: 19.924858845 Break this problem into two subproblems by setting (x + 3) equal to 19.924858845 and -19.924858845.Subproblem 1
x + 3 = 19.924858845 Simplifying x + 3 = 19.924858845 Reorder the terms: 3 + x = 19.924858845 Solving 3 + x = 19.924858845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 19.924858845 + -3 Combine like terms: 3 + -3 = 0 0 + x = 19.924858845 + -3 x = 19.924858845 + -3 Combine like terms: 19.924858845 + -3 = 16.924858845 x = 16.924858845 Simplifying x = 16.924858845Subproblem 2
x + 3 = -19.924858845 Simplifying x + 3 = -19.924858845 Reorder the terms: 3 + x = -19.924858845 Solving 3 + x = -19.924858845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -19.924858845 + -3 Combine like terms: 3 + -3 = 0 0 + x = -19.924858845 + -3 x = -19.924858845 + -3 Combine like terms: -19.924858845 + -3 = -22.924858845 x = -22.924858845 Simplifying x = -22.924858845Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.924858845, -22.924858845}
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