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Simplifying 48 = 28a + -1a2 Solving 48 = 28a + -1a2 Solving for variable 'a'. Reorder the terms: 48 + -28a + a2 = 28a + -28a + -1a2 + a2 Combine like terms: 28a + -28a = 0 48 + -28a + a2 = 0 + -1a2 + a2 48 + -28a + a2 = -1a2 + a2 Combine like terms: -1a2 + a2 = 0 48 + -28a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -28a + -48 + a2 = 0 + -48 Reorder the terms: 48 + -48 + -28a + a2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -28a + a2 = 0 + -48 -28a + a2 = 0 + -48 Combine like terms: 0 + -48 = -48 -28a + a2 = -48 The a term is -28a. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28a + 196 + a2 = -48 + 196 Reorder the terms: 196 + -28a + a2 = -48 + 196 Combine like terms: -48 + 196 = 148 196 + -28a + a2 = 148 Factor a perfect square on the left side: (a + -14)(a + -14) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (a + -14) equal to 12.165525061 and -12.165525061.Subproblem 1
a + -14 = 12.165525061 Simplifying a + -14 = 12.165525061 Reorder the terms: -14 + a = 12.165525061 Solving -14 + a = 12.165525061 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = 12.165525061 + 14 Combine like terms: -14 + 14 = 0 0 + a = 12.165525061 + 14 a = 12.165525061 + 14 Combine like terms: 12.165525061 + 14 = 26.165525061 a = 26.165525061 Simplifying a = 26.165525061Subproblem 2
a + -14 = -12.165525061 Simplifying a + -14 = -12.165525061 Reorder the terms: -14 + a = -12.165525061 Solving -14 + a = -12.165525061 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + a = -12.165525061 + 14 Combine like terms: -14 + 14 = 0 0 + a = -12.165525061 + 14 a = -12.165525061 + 14 Combine like terms: -12.165525061 + 14 = 1.834474939 a = 1.834474939 Simplifying a = 1.834474939Solution
The solution to the problem is based on the solutions from the subproblems. a = {26.165525061, 1.834474939}
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