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Simplifying 5a2 + -10a + 2 = 0 Reorder the terms: 2 + -10a + 5a2 = 0 Solving 2 + -10a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -2a + a2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2a + -0.4 + a2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2a + a2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2a + a2 = 0 + -0.4 -2a + a2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -2a + a2 = -0.4 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = -0.4 + 1 Reorder the terms: 1 + -2a + a2 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + -2a + a2 = 0.6 Factor a perfect square on the left side: (a + -1)(a + -1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (a + -1) equal to 0.774596669 and -0.774596669.Subproblem 1
a + -1 = 0.774596669 Simplifying a + -1 = 0.774596669 Reorder the terms: -1 + a = 0.774596669 Solving -1 + a = 0.774596669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 0.774596669 + 1 Combine like terms: -1 + 1 = 0 0 + a = 0.774596669 + 1 a = 0.774596669 + 1 Combine like terms: 0.774596669 + 1 = 1.774596669 a = 1.774596669 Simplifying a = 1.774596669Subproblem 2
a + -1 = -0.774596669 Simplifying a + -1 = -0.774596669 Reorder the terms: -1 + a = -0.774596669 Solving -1 + a = -0.774596669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -0.774596669 + 1 Combine like terms: -1 + 1 = 0 0 + a = -0.774596669 + 1 a = -0.774596669 + 1 Combine like terms: -0.774596669 + 1 = 0.225403331 a = 0.225403331 Simplifying a = 0.225403331Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.774596669, 0.225403331}
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