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Simplifying x2 + 6x = 377 Reorder the terms: 6x + x2 = 377 Solving 6x + x2 = 377 Solving for variable 'x'. Reorder the terms: -377 + 6x + x2 = 377 + -377 Combine like terms: 377 + -377 = 0 -377 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '377' to each side of the equation. -377 + 6x + 377 + x2 = 0 + 377 Reorder the terms: -377 + 377 + 6x + x2 = 0 + 377 Combine like terms: -377 + 377 = 0 0 + 6x + x2 = 0 + 377 6x + x2 = 0 + 377 Combine like terms: 0 + 377 = 377 6x + x2 = 377 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 = 377 + 9 Reorder the terms: 9 + 6x + x2 = 377 + 9 Combine like terms: 377 + 9 = 386 9 + 6x + x2 = 386 Factor a perfect square on the left side: (x + 3)(x + 3) = 386 Calculate the square root of the right side: 19.646882704 Break this problem into two subproblems by setting (x + 3) equal to 19.646882704 and -19.646882704.Subproblem 1
x + 3 = 19.646882704 Simplifying x + 3 = 19.646882704 Reorder the terms: 3 + x = 19.646882704 Solving 3 + x = 19.646882704 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 = 19.646882704 + -3 Combine like terms: 3 + -3 = 0 0 + x = 19.646882704 + -3 x = 19.646882704 + -3 Combine like terms: 19.646882704 + -3 = 16.646882704 x = 16.646882704 Simplifying x = 16.646882704Subproblem 2
x + 3 = -19.646882704 Simplifying x + 3 = -19.646882704 Reorder the terms: 3 + x = -19.646882704 Solving 3 + x = -19.646882704 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 = -19.646882704 + -3 Combine like terms: 3 + -3 = 0 0 + x = -19.646882704 + -3 x = -19.646882704 + -3 Combine like terms: -19.646882704 + -3 = -22.646882704 x = -22.646882704 Simplifying x = -22.646882704Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.646882704, -22.646882704}
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