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Simplifying 0.9a2 = 5.4a + -4 Reorder the terms: 0.9a2 = -4 + 5.4a Solving 0.9a2 = -4 + 5.4a Solving for variable 'a'. Reorder the terms: 4 + -5.4a + 0.9a2 = -4 + 5.4a + 4 + -5.4a Reorder the terms: 4 + -5.4a + 0.9a2 = -4 + 4 + 5.4a + -5.4a Combine like terms: -4 + 4 = 0 4 + -5.4a + 0.9a2 = 0 + 5.4a + -5.4a 4 + -5.4a + 0.9a2 = 5.4a + -5.4a Combine like terms: 5.4a + -5.4a = 0.0 4 + -5.4a + 0.9a2 = 0.0 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 = 4.555555556 9 + -6a + a2 = 4.555555556 Factor a perfect square on the left side: (a + -3)(a + -3) = 4.555555556 Calculate the square root of the right side: 2.134374746 Break this problem into two subproblems by setting (a + -3) equal to 2.134374746 and -2.134374746.Subproblem 1
a + -3 = 2.134374746 Simplifying a + -3 = 2.134374746 Reorder the terms: -3 + a = 2.134374746 Solving -3 + a = 2.134374746 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 = 2.134374746 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.134374746 + 3 a = 2.134374746 + 3 Combine like terms: 2.134374746 + 3 = 5.134374746 a = 5.134374746 Simplifying a = 5.134374746Subproblem 2
a + -3 = -2.134374746 Simplifying a + -3 = -2.134374746 Reorder the terms: -3 + a = -2.134374746 Solving -3 + a = -2.134374746 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 = -2.134374746 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.134374746 + 3 a = -2.134374746 + 3 Combine like terms: -2.134374746 + 3 = 0.865625254 a = 0.865625254 Simplifying a = 0.865625254Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.134374746, 0.865625254}
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