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Simplifying 2 = 3.24x + 4.9x2 Solving 2 = 3.24x + 4.9x2 Solving for variable 'x'. Reorder the terms: 2 + -3.24x + -4.9x2 = 3.24x + -3.24x + 4.9x2 + -4.9x2 Combine like terms: 3.24x + -3.24x = 0.00 2 + -3.24x + -4.9x2 = 0.00 + 4.9x2 + -4.9x2 2 + -3.24x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 2 + -3.24x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.4081632653 + 0.6612244898x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.6612244898x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 0.6612244898x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 0.6612244898x + x2 = 0 + 0.4081632653 0.6612244898x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 0.6612244898x + x2 = 0.4081632653 The x term is 0.6612244898x. Take half its coefficient (0.3306122449). Square it (0.1093044565) and add it to both sides. Add '0.1093044565' to each side of the equation. 0.6612244898x + 0.1093044565 + x2 = 0.4081632653 + 0.1093044565 Reorder the terms: 0.1093044565 + 0.6612244898x + x2 = 0.4081632653 + 0.1093044565 Combine like terms: 0.4081632653 + 0.1093044565 = 0.5174677218 0.1093044565 + 0.6612244898x + x2 = 0.5174677218 Factor a perfect square on the left side: (x + 0.3306122449)(x + 0.3306122449) = 0.5174677218 Calculate the square root of the right side: 0.719352293 Break this problem into two subproblems by setting (x + 0.3306122449) equal to 0.719352293 and -0.719352293.Subproblem 1
x + 0.3306122449 = 0.719352293 Simplifying x + 0.3306122449 = 0.719352293 Reorder the terms: 0.3306122449 + x = 0.719352293 Solving 0.3306122449 + x = 0.719352293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3306122449' to each side of the equation. 0.3306122449 + -0.3306122449 + x = 0.719352293 + -0.3306122449 Combine like terms: 0.3306122449 + -0.3306122449 = 0.0000000000 0.0000000000 + x = 0.719352293 + -0.3306122449 x = 0.719352293 + -0.3306122449 Combine like terms: 0.719352293 + -0.3306122449 = 0.3887400481 x = 0.3887400481 Simplifying x = 0.3887400481Subproblem 2
x + 0.3306122449 = -0.719352293 Simplifying x + 0.3306122449 = -0.719352293 Reorder the terms: 0.3306122449 + x = -0.719352293 Solving 0.3306122449 + x = -0.719352293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3306122449' to each side of the equation. 0.3306122449 + -0.3306122449 + x = -0.719352293 + -0.3306122449 Combine like terms: 0.3306122449 + -0.3306122449 = 0.0000000000 0.0000000000 + x = -0.719352293 + -0.3306122449 x = -0.719352293 + -0.3306122449 Combine like terms: -0.719352293 + -0.3306122449 = -1.0499645379 x = -1.0499645379 Simplifying x = -1.0499645379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3887400481, -1.0499645379}
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