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Simplifying 4a2 + -8a + -4 = 18a + 9a2 Reorder the terms: -4 + -8a + 4a2 = 18a + 9a2 Solving -4 + -8a + 4a2 = 18a + 9a2 Solving for variable 'a'. Reorder the terms: -4 + -8a + -18a + 4a2 + -9a2 = 18a + 9a2 + -18a + -9a2 Combine like terms: -8a + -18a = -26a -4 + -26a + 4a2 + -9a2 = 18a + 9a2 + -18a + -9a2 Combine like terms: 4a2 + -9a2 = -5a2 -4 + -26a + -5a2 = 18a + 9a2 + -18a + -9a2 Reorder the terms: -4 + -26a + -5a2 = 18a + -18a + 9a2 + -9a2 Combine like terms: 18a + -18a = 0 -4 + -26a + -5a2 = 0 + 9a2 + -9a2 -4 + -26a + -5a2 = 9a2 + -9a2 Combine like terms: 9a2 + -9a2 = 0 -4 + -26a + -5a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 26a + 5a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 26a + 5a2)' equal to zero and attempt to solve: Simplifying 4 + 26a + 5a2 = 0 Solving 4 + 26a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 5.2a + a2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 5.2a + -0.8 + a2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 5.2a + a2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 5.2a + a2 = 0 + -0.8 5.2a + a2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 5.2a + a2 = -0.8 The a term is 5.2a. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2a + 6.76 + a2 = -0.8 + 6.76 Reorder the terms: 6.76 + 5.2a + a2 = -0.8 + 6.76 Combine like terms: -0.8 + 6.76 = 5.96 6.76 + 5.2a + a2 = 5.96 Factor a perfect square on the left side: (a + 2.6)(a + 2.6) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (a + 2.6) equal to 2.441311123 and -2.441311123.Subproblem 1
a + 2.6 = 2.441311123 Simplifying a + 2.6 = 2.441311123 Reorder the terms: 2.6 + a = 2.441311123 Solving 2.6 + a = 2.441311123 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + a = 2.441311123 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + a = 2.441311123 + -2.6 a = 2.441311123 + -2.6 Combine like terms: 2.441311123 + -2.6 = -0.158688877 a = -0.158688877 Simplifying a = -0.158688877Subproblem 2
a + 2.6 = -2.441311123 Simplifying a + 2.6 = -2.441311123 Reorder the terms: 2.6 + a = -2.441311123 Solving 2.6 + a = -2.441311123 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + a = -2.441311123 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + a = -2.441311123 + -2.6 a = -2.441311123 + -2.6 Combine like terms: -2.441311123 + -2.6 = -5.041311123 a = -5.041311123 Simplifying a = -5.041311123Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.158688877, -5.041311123}Solution
a = {-0.158688877, -5.041311123}
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