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Simplifying 10a2 + -25a + 4 = 0 Reorder the terms: 4 + -25a + 10a2 = 0 Solving 4 + -25a + 10a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + -2.5a + a2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.5a + -0.4 + a2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.5a + a2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.5a + a2 = 0 + -0.4 -2.5a + a2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2.5a + a2 = -0.4 The a term is -2.5a. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5a + 1.5625 + a2 = -0.4 + 1.5625 Reorder the terms: 1.5625 + -2.5a + a2 = -0.4 + 1.5625 Combine like terms: -0.4 + 1.5625 = 1.1625 1.5625 + -2.5a + a2 = 1.1625 Factor a perfect square on the left side: (a + -1.25)(a + -1.25) = 1.1625 Calculate the square root of the right side: 1.078192933 Break this problem into two subproblems by setting (a + -1.25) equal to 1.078192933 and -1.078192933.Subproblem 1
a + -1.25 = 1.078192933 Simplifying a + -1.25 = 1.078192933 Reorder the terms: -1.25 + a = 1.078192933 Solving -1.25 + a = 1.078192933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = 1.078192933 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = 1.078192933 + 1.25 a = 1.078192933 + 1.25 Combine like terms: 1.078192933 + 1.25 = 2.328192933 a = 2.328192933 Simplifying a = 2.328192933Subproblem 2
a + -1.25 = -1.078192933 Simplifying a + -1.25 = -1.078192933 Reorder the terms: -1.25 + a = -1.078192933 Solving -1.25 + a = -1.078192933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = -1.078192933 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = -1.078192933 + 1.25 a = -1.078192933 + 1.25 Combine like terms: -1.078192933 + 1.25 = 0.171807067 a = 0.171807067 Simplifying a = 0.171807067Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.328192933, 0.171807067}
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