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Simplifying 3a2 + -78a + -12 = 0 Reorder the terms: -12 + -78a + 3a2 = 0 Solving -12 + -78a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -26a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -26a + a2)' equal to zero and attempt to solve: Simplifying -4 + -26a + a2 = 0 Solving -4 + -26a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -26a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -26a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -26a + a2 = 0 + 4 -26a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -26a + a2 = 4 The a term is -26a. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26a + 169 + a2 = 4 + 169 Reorder the terms: 169 + -26a + a2 = 4 + 169 Combine like terms: 4 + 169 = 173 169 + -26a + a2 = 173 Factor a perfect square on the left side: (a + -13)(a + -13) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (a + -13) equal to 13.152946438 and -13.152946438.Subproblem 1
a + -13 = 13.152946438 Simplifying a + -13 = 13.152946438 Reorder the terms: -13 + a = 13.152946438 Solving -13 + a = 13.152946438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + a = 13.152946438 + 13 Combine like terms: -13 + 13 = 0 0 + a = 13.152946438 + 13 a = 13.152946438 + 13 Combine like terms: 13.152946438 + 13 = 26.152946438 a = 26.152946438 Simplifying a = 26.152946438Subproblem 2
a + -13 = -13.152946438 Simplifying a + -13 = -13.152946438 Reorder the terms: -13 + a = -13.152946438 Solving -13 + a = -13.152946438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + a = -13.152946438 + 13 Combine like terms: -13 + 13 = 0 0 + a = -13.152946438 + 13 a = -13.152946438 + 13 Combine like terms: -13.152946438 + 13 = -0.152946438 a = -0.152946438 Simplifying a = -0.152946438Solution
The solution to the problem is based on the solutions from the subproblems. a = {26.152946438, -0.152946438}Solution
a = {26.152946438, -0.152946438}
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