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Simplifying x2 + 6x = 58 + 0 Reorder the terms: 6x + x2 = 58 + 0 Combine like terms: 58 + 0 = 58 6x + x2 = 58 Solving 6x + x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + 6x + x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 6x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 6x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 6x + x2 = 0 + 58 6x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 6x + x2 = 58 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 = 58 + 9 Reorder the terms: 9 + 6x + x2 = 58 + 9 Combine like terms: 58 + 9 = 67 9 + 6x + x2 = 67 Factor a perfect square on the left side: (x + 3)(x + 3) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 3) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 3 = 8.185352772 Simplifying x + 3 = 8.185352772 Reorder the terms: 3 + x = 8.185352772 Solving 3 + x = 8.185352772 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 = 8.185352772 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.185352772 + -3 x = 8.185352772 + -3 Combine like terms: 8.185352772 + -3 = 5.185352772 x = 5.185352772 Simplifying x = 5.185352772Subproblem 2
x + 3 = -8.185352772 Simplifying x + 3 = -8.185352772 Reorder the terms: 3 + x = -8.185352772 Solving 3 + x = -8.185352772 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 = -8.185352772 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.185352772 + -3 x = -8.185352772 + -3 Combine like terms: -8.185352772 + -3 = -11.185352772 x = -11.185352772 Simplifying x = -11.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.185352772, -11.185352772}
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