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Simplifying 2a2 + 9a + -20 = 0 Reorder the terms: -20 + 9a + 2a2 = 0 Solving -20 + 9a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 4.5a + a2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.5a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + 4.5a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.5a + a2 = 0 + 10 4.5a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 4.5a + a2 = 10 The a term is 4.5a. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5a + 5.0625 + a2 = 10 + 5.0625 Reorder the terms: 5.0625 + 4.5a + a2 = 10 + 5.0625 Combine like terms: 10 + 5.0625 = 15.0625 5.0625 + 4.5a + a2 = 15.0625 Factor a perfect square on the left side: (a + 2.25)(a + 2.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (a + 2.25) equal to 3.881043674 and -3.881043674.Subproblem 1
a + 2.25 = 3.881043674 Simplifying a + 2.25 = 3.881043674 Reorder the terms: 2.25 + a = 3.881043674 Solving 2.25 + a = 3.881043674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = 3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = 3.881043674 + -2.25 a = 3.881043674 + -2.25 Combine like terms: 3.881043674 + -2.25 = 1.631043674 a = 1.631043674 Simplifying a = 1.631043674Subproblem 2
a + 2.25 = -3.881043674 Simplifying a + 2.25 = -3.881043674 Reorder the terms: 2.25 + a = -3.881043674 Solving 2.25 + a = -3.881043674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = -3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = -3.881043674 + -2.25 a = -3.881043674 + -2.25 Combine like terms: -3.881043674 + -2.25 = -6.131043674 a = -6.131043674 Simplifying a = -6.131043674Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.631043674, -6.131043674}
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