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Simplifying 25a2 + -21a + 4 = 0 Reorder the terms: 4 + -21a + 25a2 = 0 Solving 4 + -21a + 25a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.16 + -0.84a + a2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -0.84a + -0.16 + a2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -0.84a + a2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -0.84a + a2 = 0 + -0.16 -0.84a + a2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -0.84a + a2 = -0.16 The a term is -0.84a. Take half its coefficient (-0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. -0.84a + 0.1764 + a2 = -0.16 + 0.1764 Reorder the terms: 0.1764 + -0.84a + a2 = -0.16 + 0.1764 Combine like terms: -0.16 + 0.1764 = 0.0164 0.1764 + -0.84a + a2 = 0.0164 Factor a perfect square on the left side: (a + -0.42)(a + -0.42) = 0.0164 Calculate the square root of the right side: 0.128062485 Break this problem into two subproblems by setting (a + -0.42) equal to 0.128062485 and -0.128062485.Subproblem 1
a + -0.42 = 0.128062485 Simplifying a + -0.42 = 0.128062485 Reorder the terms: -0.42 + a = 0.128062485 Solving -0.42 + a = 0.128062485 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.42' to each side of the equation. -0.42 + 0.42 + a = 0.128062485 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + a = 0.128062485 + 0.42 a = 0.128062485 + 0.42 Combine like terms: 0.128062485 + 0.42 = 0.548062485 a = 0.548062485 Simplifying a = 0.548062485Subproblem 2
a + -0.42 = -0.128062485 Simplifying a + -0.42 = -0.128062485 Reorder the terms: -0.42 + a = -0.128062485 Solving -0.42 + a = -0.128062485 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.42' to each side of the equation. -0.42 + 0.42 + a = -0.128062485 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + a = -0.128062485 + 0.42 a = -0.128062485 + 0.42 Combine like terms: -0.128062485 + 0.42 = 0.291937515 a = 0.291937515 Simplifying a = 0.291937515Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.548062485, 0.291937515}
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