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Simplifying 2x2 + 6x + x2 = 308 Reorder the terms: 6x + 2x2 + x2 = 308 Combine like terms: 2x2 + x2 = 3x2 6x + 3x2 = 308 Solving 6x + 3x2 = 308 Solving for variable 'x'. Reorder the terms: -308 + 6x + 3x2 = 308 + -308 Combine like terms: 308 + -308 = 0 -308 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -102.6666667 + 2x + x2 = 0 Move the constant term to the right: Add '102.6666667' to each side of the equation. -102.6666667 + 2x + 102.6666667 + x2 = 0 + 102.6666667 Reorder the terms: -102.6666667 + 102.6666667 + 2x + x2 = 0 + 102.6666667 Combine like terms: -102.6666667 + 102.6666667 = 0.0000000 0.0000000 + 2x + x2 = 0 + 102.6666667 2x + x2 = 0 + 102.6666667 Combine like terms: 0 + 102.6666667 = 102.6666667 2x + x2 = 102.6666667 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 = 102.6666667 + 1 Reorder the terms: 1 + 2x + x2 = 102.6666667 + 1 Combine like terms: 102.6666667 + 1 = 103.6666667 1 + 2x + x2 = 103.6666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 103.6666667 Calculate the square root of the right side: 10.181682901 Break this problem into two subproblems by setting (x + 1) equal to 10.181682901 and -10.181682901.Subproblem 1
x + 1 = 10.181682901 Simplifying x + 1 = 10.181682901 Reorder the terms: 1 + x = 10.181682901 Solving 1 + x = 10.181682901 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 = 10.181682901 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.181682901 + -1 x = 10.181682901 + -1 Combine like terms: 10.181682901 + -1 = 9.181682901 x = 9.181682901 Simplifying x = 9.181682901Subproblem 2
x + 1 = -10.181682901 Simplifying x + 1 = -10.181682901 Reorder the terms: 1 + x = -10.181682901 Solving 1 + x = -10.181682901 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 = -10.181682901 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.181682901 + -1 x = -10.181682901 + -1 Combine like terms: -10.181682901 + -1 = -11.181682901 x = -11.181682901 Simplifying x = -11.181682901Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.181682901, -11.181682901}
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