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Simplifying x2 + x = 308 Reorder the terms: x + x2 = 308 Solving x + x2 = 308 Solving for variable 'x'. Reorder the terms: -308 + x + x2 = 308 + -308 Combine like terms: 308 + -308 = 0 -308 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + x + x2 = 0 + 308 x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 x + x2 = 308 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 308 + 0.25 Reorder the terms: 0.25 + x + x2 = 308 + 0.25 Combine like terms: 308 + 0.25 = 308.25 0.25 + x + x2 = 308.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 308.25 Calculate the square root of the right side: 17.557049866 Break this problem into two subproblems by setting (x + 0.5) equal to 17.557049866 and -17.557049866.Subproblem 1
x + 0.5 = 17.557049866 Simplifying x + 0.5 = 17.557049866 Reorder the terms: 0.5 + x = 17.557049866 Solving 0.5 + x = 17.557049866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 17.557049866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.557049866 + -0.5 x = 17.557049866 + -0.5 Combine like terms: 17.557049866 + -0.5 = 17.057049866 x = 17.057049866 Simplifying x = 17.057049866Subproblem 2
x + 0.5 = -17.557049866 Simplifying x + 0.5 = -17.557049866 Reorder the terms: 0.5 + x = -17.557049866 Solving 0.5 + x = -17.557049866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -17.557049866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.557049866 + -0.5 x = -17.557049866 + -0.5 Combine like terms: -17.557049866 + -0.5 = -18.057049866 x = -18.057049866 Simplifying x = -18.057049866Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.057049866, -18.057049866}
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