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Simplifying a2 + -7a = 12 Reorder the terms: -7a + a2 = 12 Solving -7a + a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + -7a + a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -7a + 12 + a2 = 0 + 12 Reorder the terms: -12 + 12 + -7a + a2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -7a + a2 = 0 + 12 -7a + a2 = 0 + 12 Combine like terms: 0 + 12 = 12 -7a + a2 = 12 The a term is -7a. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7a + 12.25 + a2 = 12 + 12.25 Reorder the terms: 12.25 + -7a + a2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + -7a + a2 = 24.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (a + -3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
a + -3.5 = 4.924428901 Simplifying a + -3.5 = 4.924428901 Reorder the terms: -3.5 + a = 4.924428901 Solving -3.5 + a = 4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 4.924428901 + 3.5 a = 4.924428901 + 3.5 Combine like terms: 4.924428901 + 3.5 = 8.424428901 a = 8.424428901 Simplifying a = 8.424428901Subproblem 2
a + -3.5 = -4.924428901 Simplifying a + -3.5 = -4.924428901 Reorder the terms: -3.5 + a = -4.924428901 Solving -3.5 + a = -4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -4.924428901 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -4.924428901 + 3.5 a = -4.924428901 + 3.5 Combine like terms: -4.924428901 + 3.5 = -1.424428901 a = -1.424428901 Simplifying a = -1.424428901Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.424428901, -1.424428901}
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