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Simplifying 4a2 + -18a + 15 = 0 Reorder the terms: 15 + -18a + 4a2 = 0 Solving 15 + -18a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -4.5a + a2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -4.5a + -3.75 + a2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -4.5a + a2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -4.5a + a2 = 0 + -3.75 -4.5a + a2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -4.5a + a2 = -3.75 The a term is -4.5a. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5a + 5.0625 + a2 = -3.75 + 5.0625 Reorder the terms: 5.0625 + -4.5a + a2 = -3.75 + 5.0625 Combine like terms: -3.75 + 5.0625 = 1.3125 5.0625 + -4.5a + a2 = 1.3125 Factor a perfect square on the left side: (a + -2.25)(a + -2.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (a + -2.25) equal to 1.145643924 and -1.145643924.Subproblem 1
a + -2.25 = 1.145643924 Simplifying a + -2.25 = 1.145643924 Reorder the terms: -2.25 + a = 1.145643924 Solving -2.25 + a = 1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = 1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = 1.145643924 + 2.25 a = 1.145643924 + 2.25 Combine like terms: 1.145643924 + 2.25 = 3.395643924 a = 3.395643924 Simplifying a = 3.395643924Subproblem 2
a + -2.25 = -1.145643924 Simplifying a + -2.25 = -1.145643924 Reorder the terms: -2.25 + a = -1.145643924 Solving -2.25 + a = -1.145643924 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + a = -1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + a = -1.145643924 + 2.25 a = -1.145643924 + 2.25 Combine like terms: -1.145643924 + 2.25 = 1.104356076 a = 1.104356076 Simplifying a = 1.104356076Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.395643924, 1.104356076}
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