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Simplifying -5a(-2a + 3) + -8 = 0 Reorder the terms: -5a(3 + -2a) + -8 = 0 (3 * -5a + -2a * -5a) + -8 = 0 (-15a + 10a2) + -8 = 0 Reorder the terms: -8 + -15a + 10a2 = 0 Solving -8 + -15a + 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'. -0.8 + -1.5a + a2 = 0.0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.5a + 0.8 + a2 = 0.0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.5a + a2 = 0.0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.5a + a2 = 0.0 + 0.8 -1.5a + a2 = 0.0 + 0.8 Combine like terms: 0.0 + 0.8 = 0.8 -1.5a + a2 = 0.8 The a term is -1.5a. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5a + 0.5625 + a2 = 0.8 + 0.5625 Reorder the terms: 0.5625 + -1.5a + a2 = 0.8 + 0.5625 Combine like terms: 0.8 + 0.5625 = 1.3625 0.5625 + -1.5a + a2 = 1.3625 Factor a perfect square on the left side: (a + -0.75)(a + -0.75) = 1.3625 Calculate the square root of the right side: 1.167261753 Break this problem into two subproblems by setting (a + -0.75) equal to 1.167261753 and -1.167261753.Subproblem 1
a + -0.75 = 1.167261753 Simplifying a + -0.75 = 1.167261753 Reorder the terms: -0.75 + a = 1.167261753 Solving -0.75 + a = 1.167261753 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.167261753 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.167261753 + 0.75 a = 1.167261753 + 0.75 Combine like terms: 1.167261753 + 0.75 = 1.917261753 a = 1.917261753 Simplifying a = 1.917261753Subproblem 2
a + -0.75 = -1.167261753 Simplifying a + -0.75 = -1.167261753 Reorder the terms: -0.75 + a = -1.167261753 Solving -0.75 + a = -1.167261753 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.167261753 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.167261753 + 0.75 a = -1.167261753 + 0.75 Combine like terms: -1.167261753 + 0.75 = -0.417261753 a = -0.417261753 Simplifying a = -0.417261753Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.917261753, -0.417261753}
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