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Simplifying 15a + 9 + -15a2 = 0 Reorder the terms: 9 + 15a + -15a2 = 0 Solving 9 + 15a + -15a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 5a + -5a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 5a + -5a2)' equal to zero and attempt to solve: Simplifying 3 + 5a + -5a2 = 0 Solving 3 + 5a + -5a2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -1a + a2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1a + 0.6 + a2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1a + a2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1a + a2 = 0 + 0.6 -1a + a2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1a + a2 = 0.6 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 0.6 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 0.25 + -1a + a2 = 0.85 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (a + -0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
a + -0.5 = 0.921954446 Simplifying a + -0.5 = 0.921954446 Reorder the terms: -0.5 + a = 0.921954446 Solving -0.5 + a = 0.921954446 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 0.921954446 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 0.921954446 + 0.5 a = 0.921954446 + 0.5 Combine like terms: 0.921954446 + 0.5 = 1.421954446 a = 1.421954446 Simplifying a = 1.421954446Subproblem 2
a + -0.5 = -0.921954446 Simplifying a + -0.5 = -0.921954446 Reorder the terms: -0.5 + a = -0.921954446 Solving -0.5 + a = -0.921954446 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -0.921954446 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -0.921954446 + 0.5 a = -0.921954446 + 0.5 Combine like terms: -0.921954446 + 0.5 = -0.421954446 a = -0.421954446 Simplifying a = -0.421954446Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.421954446, -0.421954446}Solution
a = {1.421954446, -0.421954446}
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