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Simplifying 10a2 + 9a + -12 = 0 Reorder the terms: -12 + 9a + 10a2 = 0 Solving -12 + 9a + 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'. -1.2 + 0.9a + a2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.9a + 1.2 + a2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.9a + a2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.9a + a2 = 0 + 1.2 0.9a + a2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.9a + a2 = 1.2 The a term is 0.9a. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9a + 0.2025 + a2 = 1.2 + 0.2025 Reorder the terms: 0.2025 + 0.9a + a2 = 1.2 + 0.2025 Combine like terms: 1.2 + 0.2025 = 1.4025 0.2025 + 0.9a + a2 = 1.4025 Factor a perfect square on the left side: (a + 0.45)(a + 0.45) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (a + 0.45) equal to 1.184271928 and -1.184271928.Subproblem 1
a + 0.45 = 1.184271928 Simplifying a + 0.45 = 1.184271928 Reorder the terms: 0.45 + a = 1.184271928 Solving 0.45 + a = 1.184271928 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + a = 1.184271928 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = 1.184271928 + -0.45 a = 1.184271928 + -0.45 Combine like terms: 1.184271928 + -0.45 = 0.734271928 a = 0.734271928 Simplifying a = 0.734271928Subproblem 2
a + 0.45 = -1.184271928 Simplifying a + 0.45 = -1.184271928 Reorder the terms: 0.45 + a = -1.184271928 Solving 0.45 + a = -1.184271928 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + a = -1.184271928 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = -1.184271928 + -0.45 a = -1.184271928 + -0.45 Combine like terms: -1.184271928 + -0.45 = -1.634271928 a = -1.634271928 Simplifying a = -1.634271928Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.734271928, -1.634271928}
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