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Simplifying 4a2 + -48a + 52 = 0 Reorder the terms: 52 + -48a + 4a2 = 0 Solving 52 + -48a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(13 + -12a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(13 + -12a + a2)' equal to zero and attempt to solve: Simplifying 13 + -12a + a2 = 0 Solving 13 + -12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -12a + -13 + a2 = 0 + -13 Reorder the terms: 13 + -13 + -12a + a2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -12a + a2 = 0 + -13 -12a + a2 = 0 + -13 Combine like terms: 0 + -13 = -13 -12a + a2 = -13 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = -13 + 36 Reorder the terms: 36 + -12a + a2 = -13 + 36 Combine like terms: -13 + 36 = 23 36 + -12a + a2 = 23 Factor a perfect square on the left side: (a + -6)(a + -6) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (a + -6) equal to 4.795831523 and -4.795831523.Subproblem 1
a + -6 = 4.795831523 Simplifying a + -6 = 4.795831523 Reorder the terms: -6 + a = 4.795831523 Solving -6 + a = 4.795831523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + a = 4.795831523 + 6 a = 4.795831523 + 6 Combine like terms: 4.795831523 + 6 = 10.795831523 a = 10.795831523 Simplifying a = 10.795831523Subproblem 2
a + -6 = -4.795831523 Simplifying a + -6 = -4.795831523 Reorder the terms: -6 + a = -4.795831523 Solving -6 + a = -4.795831523 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + a = -4.795831523 + 6 a = -4.795831523 + 6 Combine like terms: -4.795831523 + 6 = 1.204168477 a = 1.204168477 Simplifying a = 1.204168477Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.795831523, 1.204168477}Solution
a = {10.795831523, 1.204168477}
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