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Simplifying 10a2 + -17 = -9a Reorder the terms: -17 + 10a2 = -9a Solving -17 + 10a2 = -9a Solving for variable 'a'. Reorder the terms: -17 + 9a + 10a2 = -9a + 9a Combine like terms: -9a + 9a = 0 -17 + 9a + 10a2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.7 + 0.9a + a2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + 0.9a + 1.7 + a2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + 0.9a + a2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + 0.9a + a2 = 0 + 1.7 0.9a + a2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 0.9a + a2 = 1.7 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 = 1.7 + 0.2025 Reorder the terms: 0.2025 + 0.9a + a2 = 1.7 + 0.2025 Combine like terms: 1.7 + 0.2025 = 1.9025 0.2025 + 0.9a + a2 = 1.9025 Factor a perfect square on the left side: (a + 0.45)(a + 0.45) = 1.9025 Calculate the square root of the right side: 1.379311422 Break this problem into two subproblems by setting (a + 0.45) equal to 1.379311422 and -1.379311422.Subproblem 1
a + 0.45 = 1.379311422 Simplifying a + 0.45 = 1.379311422 Reorder the terms: 0.45 + a = 1.379311422 Solving 0.45 + a = 1.379311422 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 = 1.379311422 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = 1.379311422 + -0.45 a = 1.379311422 + -0.45 Combine like terms: 1.379311422 + -0.45 = 0.929311422 a = 0.929311422 Simplifying a = 0.929311422Subproblem 2
a + 0.45 = -1.379311422 Simplifying a + 0.45 = -1.379311422 Reorder the terms: 0.45 + a = -1.379311422 Solving 0.45 + a = -1.379311422 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 = -1.379311422 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + a = -1.379311422 + -0.45 a = -1.379311422 + -0.45 Combine like terms: -1.379311422 + -0.45 = -1.829311422 a = -1.829311422 Simplifying a = -1.829311422Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.929311422, -1.829311422}
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