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Simplifying 2x2 + -20x + 59 = 98 Reorder the terms: 59 + -20x + 2x2 = 98 Solving 59 + -20x + 2x2 = 98 Solving for variable 'x'. Reorder the terms: 59 + -98 + -20x + 2x2 = 98 + -98 Combine like terms: 59 + -98 = -39 -39 + -20x + 2x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -39 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -10x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -10x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -10x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -10x + x2 = 0 + 19.5 -10x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -10x + x2 = 19.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 19.5 + 25 Reorder the terms: 25 + -10x + x2 = 19.5 + 25 Combine like terms: 19.5 + 25 = 44.5 25 + -10x + x2 = 44.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 44.5 Calculate the square root of the right side: 6.670832032 Break this problem into two subproblems by setting (x + -5) equal to 6.670832032 and -6.670832032.Subproblem 1
x + -5 = 6.670832032 Simplifying x + -5 = 6.670832032 Reorder the terms: -5 + x = 6.670832032 Solving -5 + x = 6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.670832032 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.670832032 + 5 x = 6.670832032 + 5 Combine like terms: 6.670832032 + 5 = 11.670832032 x = 11.670832032 Simplifying x = 11.670832032Subproblem 2
x + -5 = -6.670832032 Simplifying x + -5 = -6.670832032 Reorder the terms: -5 + x = -6.670832032 Solving -5 + x = -6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.670832032 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.670832032 + 5 x = -6.670832032 + 5 Combine like terms: -6.670832032 + 5 = -1.670832032 x = -1.670832032 Simplifying x = -1.670832032Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.670832032, -1.670832032}
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