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Simplifying x2 + 2x + -308 = 0 Reorder the terms: -308 + 2x + x2 = 0 Solving -308 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + 2x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + 2x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 2x + x2 = 0 + 308 2x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 2x + x2 = 308 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 = 308 + 1 Reorder the terms: 1 + 2x + x2 = 308 + 1 Combine like terms: 308 + 1 = 309 1 + 2x + x2 = 309 Factor a perfect square on the left side: (x + 1)(x + 1) = 309 Calculate the square root of the right side: 17.578395831 Break this problem into two subproblems by setting (x + 1) equal to 17.578395831 and -17.578395831.Subproblem 1
x + 1 = 17.578395831 Simplifying x + 1 = 17.578395831 Reorder the terms: 1 + x = 17.578395831 Solving 1 + x = 17.578395831 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 = 17.578395831 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.578395831 + -1 x = 17.578395831 + -1 Combine like terms: 17.578395831 + -1 = 16.578395831 x = 16.578395831 Simplifying x = 16.578395831Subproblem 2
x + 1 = -17.578395831 Simplifying x + 1 = -17.578395831 Reorder the terms: 1 + x = -17.578395831 Solving 1 + x = -17.578395831 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 = -17.578395831 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.578395831 + -1 x = -17.578395831 + -1 Combine like terms: -17.578395831 + -1 = -18.578395831 x = -18.578395831 Simplifying x = -18.578395831Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.578395831, -18.578395831}
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