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Simplifying 4a2 + -12a + -60 = 0 Reorder the terms: -60 + -12a + 4a2 = 0 Solving -60 + -12a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -3a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -3a + a2)' equal to zero and attempt to solve: Simplifying -15 + -3a + a2 = 0 Solving -15 + -3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -3a + 15 + a2 = 0 + 15 Reorder the terms: -15 + 15 + -3a + a2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3a + a2 = 0 + 15 -3a + a2 = 0 + 15 Combine like terms: 0 + 15 = 15 -3a + a2 = 15 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = 15 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 15 + 2.25 Combine like terms: 15 + 2.25 = 17.25 2.25 + -3a + a2 = 17.25 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (a + -1.5) equal to 4.153311931 and -4.153311931.Subproblem 1
a + -1.5 = 4.153311931 Simplifying a + -1.5 = 4.153311931 Reorder the terms: -1.5 + a = 4.153311931 Solving -1.5 + a = 4.153311931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 4.153311931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 4.153311931 + 1.5 a = 4.153311931 + 1.5 Combine like terms: 4.153311931 + 1.5 = 5.653311931 a = 5.653311931 Simplifying a = 5.653311931Subproblem 2
a + -1.5 = -4.153311931 Simplifying a + -1.5 = -4.153311931 Reorder the terms: -1.5 + a = -4.153311931 Solving -1.5 + a = -4.153311931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -4.153311931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -4.153311931 + 1.5 a = -4.153311931 + 1.5 Combine like terms: -4.153311931 + 1.5 = -2.653311931 a = -2.653311931 Simplifying a = -2.653311931Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.653311931, -2.653311931}Solution
a = {5.653311931, -2.653311931}
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