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Simplifying 6a * 5a + 2a + -9 = 0 Reorder the terms for easier multiplication: 6 * 5a * a + 2a + -9 = 0 Multiply 6 * 5 30a * a + 2a + -9 = 0 Multiply a * a 30a2 + 2a + -9 = 0 Reorder the terms: -9 + 2a + 30a2 = 0 Solving -9 + 2a + 30a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.3 + 0.06666666667a + a2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.06666666667a + 0.3 + a2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.06666666667a + a2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.06666666667a + a2 = 0.0 + 0.3 0.06666666667a + a2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.06666666667a + a2 = 0.3 The a term is 0.06666666667a. Take half its coefficient (0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. 0.06666666667a + 0.001111111112 + a2 = 0.3 + 0.001111111112 Reorder the terms: 0.001111111112 + 0.06666666667a + a2 = 0.3 + 0.001111111112 Combine like terms: 0.3 + 0.001111111112 = 0.301111111112 0.001111111112 + 0.06666666667a + a2 = 0.301111111112 Factor a perfect square on the left side: (a + 0.03333333334)(a + 0.03333333334) = 0.301111111112 Calculate the square root of the right side: 0.548735921 Break this problem into two subproblems by setting (a + 0.03333333334) equal to 0.548735921 and -0.548735921.Subproblem 1
a + 0.03333333334 = 0.548735921 Simplifying a + 0.03333333334 = 0.548735921 Reorder the terms: 0.03333333334 + a = 0.548735921 Solving 0.03333333334 + a = 0.548735921 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + a = 0.548735921 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + a = 0.548735921 + -0.03333333334 a = 0.548735921 + -0.03333333334 Combine like terms: 0.548735921 + -0.03333333334 = 0.51540258766 a = 0.51540258766 Simplifying a = 0.51540258766Subproblem 2
a + 0.03333333334 = -0.548735921 Simplifying a + 0.03333333334 = -0.548735921 Reorder the terms: 0.03333333334 + a = -0.548735921 Solving 0.03333333334 + a = -0.548735921 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + a = -0.548735921 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + a = -0.548735921 + -0.03333333334 a = -0.548735921 + -0.03333333334 Combine like terms: -0.548735921 + -0.03333333334 = -0.58206925434 a = -0.58206925434 Simplifying a = -0.58206925434Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.51540258766, -0.58206925434}
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