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Simplifying 2x2 + -20x = -49 Reorder the terms: -20x + 2x2 = -49 Solving -20x + 2x2 = -49 Solving for variable 'x'. Reorder the terms: 49 + -20x + 2x2 = -49 + 49 Combine like terms: -49 + 49 = 0 49 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24.5 + -10x + x2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + -10x + -24.5 + x2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + -10x + x2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -10x + x2 = 0 + -24.5 -10x + x2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 -10x + x2 = -24.5 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 = -24.5 + 25 Reorder the terms: 25 + -10x + x2 = -24.5 + 25 Combine like terms: -24.5 + 25 = 0.5 25 + -10x + x2 = 0.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -5) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -5 = 0.707106781 Simplifying x + -5 = 0.707106781 Reorder the terms: -5 + x = 0.707106781 Solving -5 + x = 0.707106781 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 = 0.707106781 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0.707106781 + 5 x = 0.707106781 + 5 Combine like terms: 0.707106781 + 5 = 5.707106781 x = 5.707106781 Simplifying x = 5.707106781Subproblem 2
x + -5 = -0.707106781 Simplifying x + -5 = -0.707106781 Reorder the terms: -5 + x = -0.707106781 Solving -5 + x = -0.707106781 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 = -0.707106781 + 5 Combine like terms: -5 + 5 = 0 0 + x = -0.707106781 + 5 x = -0.707106781 + 5 Combine like terms: -0.707106781 + 5 = 4.292893219 x = 4.292893219 Simplifying x = 4.292893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.707106781, 4.292893219}
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