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Simplifying -1a2 + 30 + 40a = 5 + 4a Reorder the terms: 30 + 40a + -1a2 = 5 + 4a Solving 30 + 40a + -1a2 = 5 + 4a Solving for variable 'a'. Reorder the terms: 30 + -5 + 40a + -4a + -1a2 = 5 + 4a + -5 + -4a Combine like terms: 30 + -5 = 25 25 + 40a + -4a + -1a2 = 5 + 4a + -5 + -4a Combine like terms: 40a + -4a = 36a 25 + 36a + -1a2 = 5 + 4a + -5 + -4a Reorder the terms: 25 + 36a + -1a2 = 5 + -5 + 4a + -4a Combine like terms: 5 + -5 = 0 25 + 36a + -1a2 = 0 + 4a + -4a 25 + 36a + -1a2 = 4a + -4a Combine like terms: 4a + -4a = 0 25 + 36a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -36a + a2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -36a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + -36a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -36a + a2 = 0 + 25 -36a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 -36a + a2 = 25 The a term is -36a. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36a + 324 + a2 = 25 + 324 Reorder the terms: 324 + -36a + a2 = 25 + 324 Combine like terms: 25 + 324 = 349 324 + -36a + a2 = 349 Factor a perfect square on the left side: (a + -18)(a + -18) = 349 Calculate the square root of the right side: 18.681541692 Break this problem into two subproblems by setting (a + -18) equal to 18.681541692 and -18.681541692.Subproblem 1
a + -18 = 18.681541692 Simplifying a + -18 = 18.681541692 Reorder the terms: -18 + a = 18.681541692 Solving -18 + a = 18.681541692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + a = 18.681541692 + 18 Combine like terms: -18 + 18 = 0 0 + a = 18.681541692 + 18 a = 18.681541692 + 18 Combine like terms: 18.681541692 + 18 = 36.681541692 a = 36.681541692 Simplifying a = 36.681541692Subproblem 2
a + -18 = -18.681541692 Simplifying a + -18 = -18.681541692 Reorder the terms: -18 + a = -18.681541692 Solving -18 + a = -18.681541692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + a = -18.681541692 + 18 Combine like terms: -18 + 18 = 0 0 + a = -18.681541692 + 18 a = -18.681541692 + 18 Combine like terms: -18.681541692 + 18 = -0.681541692 a = -0.681541692 Simplifying a = -0.681541692Solution
The solution to the problem is based on the solutions from the subproblems. a = {36.681541692, -0.681541692}
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