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Simplifying 5(a2 + -20a + -60) = 0 Reorder the terms: 5(-60 + -20a + a2) = 0 (-60 * 5 + -20a * 5 + a2 * 5) = 0 (-300 + -100a + 5a2) = 0 Solving -300 + -100a + 5a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(-60 + -20a + a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-60 + -20a + a2)' equal to zero and attempt to solve: Simplifying -60 + -20a + a2 = 0 Solving -60 + -20a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -20a + 60 + a2 = 0 + 60 Reorder the terms: -60 + 60 + -20a + a2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -20a + a2 = 0 + 60 -20a + a2 = 0 + 60 Combine like terms: 0 + 60 = 60 -20a + a2 = 60 The a term is -20a. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20a + 100 + a2 = 60 + 100 Reorder the terms: 100 + -20a + a2 = 60 + 100 Combine like terms: 60 + 100 = 160 100 + -20a + a2 = 160 Factor a perfect square on the left side: (a + -10)(a + -10) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (a + -10) equal to 12.649110641 and -12.649110641.Subproblem 1
a + -10 = 12.649110641 Simplifying a + -10 = 12.649110641 Reorder the terms: -10 + a = 12.649110641 Solving -10 + a = 12.649110641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = 12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + a = 12.649110641 + 10 a = 12.649110641 + 10 Combine like terms: 12.649110641 + 10 = 22.649110641 a = 22.649110641 Simplifying a = 22.649110641Subproblem 2
a + -10 = -12.649110641 Simplifying a + -10 = -12.649110641 Reorder the terms: -10 + a = -12.649110641 Solving -10 + a = -12.649110641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + a = -12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + a = -12.649110641 + 10 a = -12.649110641 + 10 Combine like terms: -12.649110641 + 10 = -2.649110641 a = -2.649110641 Simplifying a = -2.649110641Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.649110641, -2.649110641}Solution
a = {22.649110641, -2.649110641}
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