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Simplifying 2x2 + -50x + 21 = 0 Reorder the terms: 21 + -50x + 2x2 = 0 Solving 21 + -50x + 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'. 10.5 + -25x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -25x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -25x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -25x + x2 = 0 + -10.5 -25x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -25x + x2 = -10.5 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -10.5 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -10.5 + 156.25 Combine like terms: -10.5 + 156.25 = 145.75 156.25 + -25x + x2 = 145.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 145.75 Calculate the square root of the right side: 12.072696468 Break this problem into two subproblems by setting (x + -12.5) equal to 12.072696468 and -12.072696468.Subproblem 1
x + -12.5 = 12.072696468 Simplifying x + -12.5 = 12.072696468 Reorder the terms: -12.5 + x = 12.072696468 Solving -12.5 + x = 12.072696468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 12.072696468 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 12.072696468 + 12.5 x = 12.072696468 + 12.5 Combine like terms: 12.072696468 + 12.5 = 24.572696468 x = 24.572696468 Simplifying x = 24.572696468Subproblem 2
x + -12.5 = -12.072696468 Simplifying x + -12.5 = -12.072696468 Reorder the terms: -12.5 + x = -12.072696468 Solving -12.5 + x = -12.072696468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -12.072696468 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -12.072696468 + 12.5 x = -12.072696468 + 12.5 Combine like terms: -12.072696468 + 12.5 = 0.427303532 x = 0.427303532 Simplifying x = 0.427303532Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.572696468, 0.427303532}
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