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Simplifying 20X2 + -49X + 25 = 0 Reorder the terms: 25 + -49X + 20X2 = 0 Solving 25 + -49X + 20X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.25 + -2.45X + X2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2.45X + -1.25 + X2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2.45X + X2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2.45X + X2 = 0 + -1.25 -2.45X + X2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2.45X + X2 = -1.25 The X term is -2.45X. Take half its coefficient (-1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. -2.45X + 1.500625 + X2 = -1.25 + 1.500625 Reorder the terms: 1.500625 + -2.45X + X2 = -1.25 + 1.500625 Combine like terms: -1.25 + 1.500625 = 0.250625 1.500625 + -2.45X + X2 = 0.250625 Factor a perfect square on the left side: (X + -1.225)(X + -1.225) = 0.250625 Calculate the square root of the right side: 0.50062461 Break this problem into two subproblems by setting (X + -1.225) equal to 0.50062461 and -0.50062461.Subproblem 1
X + -1.225 = 0.50062461 Simplifying X + -1.225 = 0.50062461 Reorder the terms: -1.225 + X = 0.50062461 Solving -1.225 + X = 0.50062461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + X = 0.50062461 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + X = 0.50062461 + 1.225 X = 0.50062461 + 1.225 Combine like terms: 0.50062461 + 1.225 = 1.72562461 X = 1.72562461 Simplifying X = 1.72562461Subproblem 2
X + -1.225 = -0.50062461 Simplifying X + -1.225 = -0.50062461 Reorder the terms: -1.225 + X = -0.50062461 Solving -1.225 + X = -0.50062461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + X = -0.50062461 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + X = -0.50062461 + 1.225 X = -0.50062461 + 1.225 Combine like terms: -0.50062461 + 1.225 = 0.72437539 X = 0.72437539 Simplifying X = 0.72437539Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.72562461, 0.72437539}
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