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Simplifying x2 + 2x + 6 = 313 Reorder the terms: 6 + 2x + x2 = 313 Solving 6 + 2x + x2 = 313 Solving for variable 'x'. Reorder the terms: 6 + -313 + 2x + x2 = 313 + -313 Combine like terms: 6 + -313 = -307 -307 + 2x + x2 = 313 + -313 Combine like terms: 313 + -313 = 0 -307 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '307' to each side of the equation. -307 + 2x + 307 + x2 = 0 + 307 Reorder the terms: -307 + 307 + 2x + x2 = 0 + 307 Combine like terms: -307 + 307 = 0 0 + 2x + x2 = 0 + 307 2x + x2 = 0 + 307 Combine like terms: 0 + 307 = 307 2x + x2 = 307 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 307 + 1 Reorder the terms: 1 + 2x + x2 = 307 + 1 Combine like terms: 307 + 1 = 308 1 + 2x + x2 = 308 Factor a perfect square on the left side: (x + 1)(x + 1) = 308 Calculate the square root of the right side: 17.549928775 Break this problem into two subproblems by setting (x + 1) equal to 17.549928775 and -17.549928775.Subproblem 1
x + 1 = 17.549928775 Simplifying x + 1 = 17.549928775 Reorder the terms: 1 + x = 17.549928775 Solving 1 + x = 17.549928775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 17.549928775 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.549928775 + -1 x = 17.549928775 + -1 Combine like terms: 17.549928775 + -1 = 16.549928775 x = 16.549928775 Simplifying x = 16.549928775Subproblem 2
x + 1 = -17.549928775 Simplifying x + 1 = -17.549928775 Reorder the terms: 1 + x = -17.549928775 Solving 1 + x = -17.549928775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -17.549928775 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.549928775 + -1 x = -17.549928775 + -1 Combine like terms: -17.549928775 + -1 = -18.549928775 x = -18.549928775 Simplifying x = -18.549928775Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.549928775, -18.549928775}
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