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Simplifying 5a2 + -9a + -8 = 0 Reorder the terms: -8 + -9a + 5a2 = 0 Solving -8 + -9a + 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'. -1.6 + -1.8a + a2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.8a + 1.6 + a2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.8a + a2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.8a + a2 = 0 + 1.6 -1.8a + a2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.8a + a2 = 1.6 The a term is -1.8a. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8a + 0.81 + a2 = 1.6 + 0.81 Reorder the terms: 0.81 + -1.8a + a2 = 1.6 + 0.81 Combine like terms: 1.6 + 0.81 = 2.41 0.81 + -1.8a + a2 = 2.41 Factor a perfect square on the left side: (a + -0.9)(a + -0.9) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (a + -0.9) equal to 1.55241747 and -1.55241747.Subproblem 1
a + -0.9 = 1.55241747 Simplifying a + -0.9 = 1.55241747 Reorder the terms: -0.9 + a = 1.55241747 Solving -0.9 + a = 1.55241747 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + a = 1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + a = 1.55241747 + 0.9 a = 1.55241747 + 0.9 Combine like terms: 1.55241747 + 0.9 = 2.45241747 a = 2.45241747 Simplifying a = 2.45241747Subproblem 2
a + -0.9 = -1.55241747 Simplifying a + -0.9 = -1.55241747 Reorder the terms: -0.9 + a = -1.55241747 Solving -0.9 + a = -1.55241747 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + a = -1.55241747 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + a = -1.55241747 + 0.9 a = -1.55241747 + 0.9 Combine like terms: -1.55241747 + 0.9 = -0.65241747 a = -0.65241747 Simplifying a = -0.65241747Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.45241747, -0.65241747}
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