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Simplifying 4x2 + -141x + 25 = 0 Reorder the terms: 25 + -141x + 4x2 = 0 Solving 25 + -141x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -35.25x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -35.25x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -35.25x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -35.25x + x2 = 0 + -6.25 -35.25x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -35.25x + x2 = -6.25 The x term is -35.25x. Take half its coefficient (-17.625). Square it (310.640625) and add it to both sides. Add '310.640625' to each side of the equation. -35.25x + 310.640625 + x2 = -6.25 + 310.640625 Reorder the terms: 310.640625 + -35.25x + x2 = -6.25 + 310.640625 Combine like terms: -6.25 + 310.640625 = 304.390625 310.640625 + -35.25x + x2 = 304.390625 Factor a perfect square on the left side: (x + -17.625)(x + -17.625) = 304.390625 Calculate the square root of the right side: 17.446794118 Break this problem into two subproblems by setting (x + -17.625) equal to 17.446794118 and -17.446794118.Subproblem 1
x + -17.625 = 17.446794118 Simplifying x + -17.625 = 17.446794118 Reorder the terms: -17.625 + x = 17.446794118 Solving -17.625 + x = 17.446794118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.625' to each side of the equation. -17.625 + 17.625 + x = 17.446794118 + 17.625 Combine like terms: -17.625 + 17.625 = 0.000 0.000 + x = 17.446794118 + 17.625 x = 17.446794118 + 17.625 Combine like terms: 17.446794118 + 17.625 = 35.071794118 x = 35.071794118 Simplifying x = 35.071794118Subproblem 2
x + -17.625 = -17.446794118 Simplifying x + -17.625 = -17.446794118 Reorder the terms: -17.625 + x = -17.446794118 Solving -17.625 + x = -17.446794118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.625' to each side of the equation. -17.625 + 17.625 + x = -17.446794118 + 17.625 Combine like terms: -17.625 + 17.625 = 0.000 0.000 + x = -17.446794118 + 17.625 x = -17.446794118 + 17.625 Combine like terms: -17.446794118 + 17.625 = 0.178205882 x = 0.178205882 Simplifying x = 0.178205882Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.071794118, 0.178205882}
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