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Simplifying 15a2 + -3a + -8 = 0 Reorder the terms: -8 + -3a + 15a2 = 0 Solving -8 + -3a + 15a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + -0.2a + a2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + -0.2a + 0.5333333333 + a2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + -0.2a + a2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + -0.2a + a2 = 0 + 0.5333333333 -0.2a + a2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 -0.2a + a2 = 0.5333333333 The a term is -0.2a. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2a + 0.01 + a2 = 0.5333333333 + 0.01 Reorder the terms: 0.01 + -0.2a + a2 = 0.5333333333 + 0.01 Combine like terms: 0.5333333333 + 0.01 = 0.5433333333 0.01 + -0.2a + a2 = 0.5433333333 Factor a perfect square on the left side: (a + -0.1)(a + -0.1) = 0.5433333333 Calculate the square root of the right side: 0.73711148 Break this problem into two subproblems by setting (a + -0.1) equal to 0.73711148 and -0.73711148.Subproblem 1
a + -0.1 = 0.73711148 Simplifying a + -0.1 = 0.73711148 Reorder the terms: -0.1 + a = 0.73711148 Solving -0.1 + a = 0.73711148 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = 0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = 0.73711148 + 0.1 a = 0.73711148 + 0.1 Combine like terms: 0.73711148 + 0.1 = 0.83711148 a = 0.83711148 Simplifying a = 0.83711148Subproblem 2
a + -0.1 = -0.73711148 Simplifying a + -0.1 = -0.73711148 Reorder the terms: -0.1 + a = -0.73711148 Solving -0.1 + a = -0.73711148 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = -0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = -0.73711148 + 0.1 a = -0.73711148 + 0.1 Combine like terms: -0.73711148 + 0.1 = -0.63711148 a = -0.63711148 Simplifying a = -0.63711148Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.83711148, -0.63711148}
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