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Simplifying 2x2 + 4x = 621 Reorder the terms: 4x + 2x2 = 621 Solving 4x + 2x2 = 621 Solving for variable 'x'. Reorder the terms: -621 + 4x + 2x2 = 621 + -621 Combine like terms: 621 + -621 = 0 -621 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -310.5 + 2x + x2 = 0 Move the constant term to the right: Add '310.5' to each side of the equation. -310.5 + 2x + 310.5 + x2 = 0 + 310.5 Reorder the terms: -310.5 + 310.5 + 2x + x2 = 0 + 310.5 Combine like terms: -310.5 + 310.5 = 0.0 0.0 + 2x + x2 = 0 + 310.5 2x + x2 = 0 + 310.5 Combine like terms: 0 + 310.5 = 310.5 2x + x2 = 310.5 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 = 310.5 + 1 Reorder the terms: 1 + 2x + x2 = 310.5 + 1 Combine like terms: 310.5 + 1 = 311.5 1 + 2x + x2 = 311.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 311.5 Calculate the square root of the right side: 17.649362595 Break this problem into two subproblems by setting (x + 1) equal to 17.649362595 and -17.649362595.Subproblem 1
x + 1 = 17.649362595 Simplifying x + 1 = 17.649362595 Reorder the terms: 1 + x = 17.649362595 Solving 1 + x = 17.649362595 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 = 17.649362595 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.649362595 + -1 x = 17.649362595 + -1 Combine like terms: 17.649362595 + -1 = 16.649362595 x = 16.649362595 Simplifying x = 16.649362595Subproblem 2
x + 1 = -17.649362595 Simplifying x + 1 = -17.649362595 Reorder the terms: 1 + x = -17.649362595 Solving 1 + x = -17.649362595 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 = -17.649362595 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.649362595 + -1 x = -17.649362595 + -1 Combine like terms: -17.649362595 + -1 = -18.649362595 x = -18.649362595 Simplifying x = -18.649362595Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.649362595, -18.649362595}
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