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Simplifying 5 + a(a + -8) = 4 + 13a Reorder the terms: 5 + a(-8 + a) = 4 + 13a 5 + (-8 * a + a * a) = 4 + 13a 5 + (-8a + a2) = 4 + 13a Solving 5 + -8a + a2 = 4 + 13a Solving for variable 'a'. Reorder the terms: 5 + -4 + -8a + -13a + a2 = 4 + 13a + -4 + -13a Combine like terms: 5 + -4 = 1 1 + -8a + -13a + a2 = 4 + 13a + -4 + -13a Combine like terms: -8a + -13a = -21a 1 + -21a + a2 = 4 + 13a + -4 + -13a Reorder the terms: 1 + -21a + a2 = 4 + -4 + 13a + -13a Combine like terms: 4 + -4 = 0 1 + -21a + a2 = 0 + 13a + -13a 1 + -21a + a2 = 13a + -13a Combine like terms: 13a + -13a = 0 1 + -21a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -21a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -21a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -21a + a2 = 0 + -1 -21a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -21a + a2 = -1 The a term is -21a. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21a + 110.25 + a2 = -1 + 110.25 Reorder the terms: 110.25 + -21a + a2 = -1 + 110.25 Combine like terms: -1 + 110.25 = 109.25 110.25 + -21a + a2 = 109.25 Factor a perfect square on the left side: (a + -10.5)(a + -10.5) = 109.25 Calculate the square root of the right side: 10.45227248 Break this problem into two subproblems by setting (a + -10.5) equal to 10.45227248 and -10.45227248.Subproblem 1
a + -10.5 = 10.45227248 Simplifying a + -10.5 = 10.45227248 Reorder the terms: -10.5 + a = 10.45227248 Solving -10.5 + a = 10.45227248 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = 10.45227248 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 10.45227248 + 10.5 a = 10.45227248 + 10.5 Combine like terms: 10.45227248 + 10.5 = 20.95227248 a = 20.95227248 Simplifying a = 20.95227248Subproblem 2
a + -10.5 = -10.45227248 Simplifying a + -10.5 = -10.45227248 Reorder the terms: -10.5 + a = -10.45227248 Solving -10.5 + a = -10.45227248 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + a = -10.45227248 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -10.45227248 + 10.5 a = -10.45227248 + 10.5 Combine like terms: -10.45227248 + 10.5 = 0.04772752 a = 0.04772752 Simplifying a = 0.04772752Solution
The solution to the problem is based on the solutions from the subproblems. a = {20.95227248, 0.04772752}
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