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Simplifying 2x2 + -49x + -910 = 0 Reorder the terms: -910 + -49x + 2x2 = 0 Solving -910 + -49x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -455 + -24.5x + x2 = 0 Move the constant term to the right: Add '455' to each side of the equation. -455 + -24.5x + 455 + x2 = 0 + 455 Reorder the terms: -455 + 455 + -24.5x + x2 = 0 + 455 Combine like terms: -455 + 455 = 0 0 + -24.5x + x2 = 0 + 455 -24.5x + x2 = 0 + 455 Combine like terms: 0 + 455 = 455 -24.5x + x2 = 455 The x term is -24.5x. Take half its coefficient (-12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. -24.5x + 150.0625 + x2 = 455 + 150.0625 Reorder the terms: 150.0625 + -24.5x + x2 = 455 + 150.0625 Combine like terms: 455 + 150.0625 = 605.0625 150.0625 + -24.5x + x2 = 605.0625 Factor a perfect square on the left side: (x + -12.25)(x + -12.25) = 605.0625 Calculate the square root of the right side: 24.598018213 Break this problem into two subproblems by setting (x + -12.25) equal to 24.598018213 and -24.598018213.Subproblem 1
x + -12.25 = 24.598018213 Simplifying x + -12.25 = 24.598018213 Reorder the terms: -12.25 + x = 24.598018213 Solving -12.25 + x = 24.598018213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = 24.598018213 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = 24.598018213 + 12.25 x = 24.598018213 + 12.25 Combine like terms: 24.598018213 + 12.25 = 36.848018213 x = 36.848018213 Simplifying x = 36.848018213Subproblem 2
x + -12.25 = -24.598018213 Simplifying x + -12.25 = -24.598018213 Reorder the terms: -12.25 + x = -24.598018213 Solving -12.25 + x = -24.598018213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.25' to each side of the equation. -12.25 + 12.25 + x = -24.598018213 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x = -24.598018213 + 12.25 x = -24.598018213 + 12.25 Combine like terms: -24.598018213 + 12.25 = -12.348018213 x = -12.348018213 Simplifying x = -12.348018213Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.848018213, -12.348018213}
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