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Simplifying x2 + 6x = 349 Reorder the terms: 6x + x2 = 349 Solving 6x + x2 = 349 Solving for variable 'x'. Reorder the terms: -349 + 6x + x2 = 349 + -349 Combine like terms: 349 + -349 = 0 -349 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '349' to each side of the equation. -349 + 6x + 349 + x2 = 0 + 349 Reorder the terms: -349 + 349 + 6x + x2 = 0 + 349 Combine like terms: -349 + 349 = 0 0 + 6x + x2 = 0 + 349 6x + x2 = 0 + 349 Combine like terms: 0 + 349 = 349 6x + x2 = 349 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 = 349 + 9 Reorder the terms: 9 + 6x + x2 = 349 + 9 Combine like terms: 349 + 9 = 358 9 + 6x + x2 = 358 Factor a perfect square on the left side: (x + 3)(x + 3) = 358 Calculate the square root of the right side: 18.920887928 Break this problem into two subproblems by setting (x + 3) equal to 18.920887928 and -18.920887928.Subproblem 1
x + 3 = 18.920887928 Simplifying x + 3 = 18.920887928 Reorder the terms: 3 + x = 18.920887928 Solving 3 + x = 18.920887928 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 = 18.920887928 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.920887928 + -3 x = 18.920887928 + -3 Combine like terms: 18.920887928 + -3 = 15.920887928 x = 15.920887928 Simplifying x = 15.920887928Subproblem 2
x + 3 = -18.920887928 Simplifying x + 3 = -18.920887928 Reorder the terms: 3 + x = -18.920887928 Solving 3 + x = -18.920887928 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 = -18.920887928 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.920887928 + -3 x = -18.920887928 + -3 Combine like terms: -18.920887928 + -3 = -21.920887928 x = -21.920887928 Simplifying x = -21.920887928Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.920887928, -21.920887928}
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