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Simplifying a2 + -7a = -7 Reorder the terms: -7a + a2 = -7 Solving -7a + a2 = -7 Solving for variable 'a'. Reorder the terms: 7 + -7a + a2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -7a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -7a + -7 + a2 = 0 + -7 Reorder the terms: 7 + -7 + -7a + a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -7a + a2 = 0 + -7 -7a + a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -7a + a2 = -7 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 = -7 + 12.25 Reorder the terms: 12.25 + -7a + a2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + -7a + a2 = 5.25 Factor a perfect square on the left side: (a + -3.5)(a + -3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (a + -3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
a + -3.5 = 2.291287847 Simplifying a + -3.5 = 2.291287847 Reorder the terms: -3.5 + a = 2.291287847 Solving -3.5 + a = 2.291287847 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 = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 2.291287847 + 3.5 a = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 a = 5.791287847 Simplifying a = 5.791287847Subproblem 2
a + -3.5 = -2.291287847 Simplifying a + -3.5 = -2.291287847 Reorder the terms: -3.5 + a = -2.291287847 Solving -3.5 + a = -2.291287847 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 = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -2.291287847 + 3.5 a = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 a = 1.208712153 Simplifying a = 1.208712153Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.791287847, 1.208712153}
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