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Simplifying 0.9a2 + 5.4a + -4 = 0 Reorder the terms: -4 + 5.4a + 0.9a2 = 0 Solving -4 + 5.4a + 0.9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -4.444444444 + 6a + a2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + 6a + 4.444444444 + a2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + 6a + a2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + 6a + a2 = 0 + 4.444444444 6a + a2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 6a + a2 = 4.444444444 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 4.444444444 + 9 Reorder the terms: 9 + 6a + a2 = 4.444444444 + 9 Combine like terms: 4.444444444 + 9 = 13.444444444 9 + 6a + a2 = 13.444444444 Factor a perfect square on the left side: (a + 3)(a + 3) = 13.444444444 Calculate the square root of the right side: 3.666666667 Break this problem into two subproblems by setting (a + 3) equal to 3.666666667 and -3.666666667.Subproblem 1
a + 3 = 3.666666667 Simplifying a + 3 = 3.666666667 Reorder the terms: 3 + a = 3.666666667 Solving 3 + a = 3.666666667 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 3.666666667 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.666666667 + -3 a = 3.666666667 + -3 Combine like terms: 3.666666667 + -3 = 0.666666667 a = 0.666666667 Simplifying a = 0.666666667Subproblem 2
a + 3 = -3.666666667 Simplifying a + 3 = -3.666666667 Reorder the terms: 3 + a = -3.666666667 Solving 3 + a = -3.666666667 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -3.666666667 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.666666667 + -3 a = -3.666666667 + -3 Combine like terms: -3.666666667 + -3 = -6.666666667 a = -6.666666667 Simplifying a = -6.666666667Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.666666667, -6.666666667}
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