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Simplifying 4 + 10a + a2 + -3(a + 2) + -13 = 0 Reorder the terms: 4 + 10a + a2 + -3(2 + a) + -13 = 0 4 + 10a + a2 + (2 * -3 + a * -3) + -13 = 0 4 + 10a + a2 + (-6 + -3a) + -13 = 0 Reorder the terms: 4 + -6 + -13 + 10a + -3a + a2 = 0 Combine like terms: 4 + -6 = -2 -2 + -13 + 10a + -3a + a2 = 0 Combine like terms: -2 + -13 = -15 -15 + 10a + -3a + a2 = 0 Combine like terms: 10a + -3a = 7a -15 + 7a + a2 = 0 Solving -15 + 7a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 7a + 15 + a2 = 0 + 15 Reorder the terms: -15 + 15 + 7a + a2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7a + a2 = 0 + 15 7a + a2 = 0 + 15 Combine like terms: 0 + 15 = 15 7a + a2 = 15 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 = 15 + 12.25 Reorder the terms: 12.25 + 7a + a2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7a + a2 = 27.25 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (a + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
a + 3.5 = 5.220153254 Simplifying a + 3.5 = 5.220153254 Reorder the terms: 3.5 + a = 5.220153254 Solving 3.5 + a = 5.220153254 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 = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 5.220153254 + -3.5 a = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 a = 1.720153254 Simplifying a = 1.720153254Subproblem 2
a + 3.5 = -5.220153254 Simplifying a + 3.5 = -5.220153254 Reorder the terms: 3.5 + a = -5.220153254 Solving 3.5 + a = -5.220153254 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 = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -5.220153254 + -3.5 a = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 a = -8.720153254 Simplifying a = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.720153254, -8.720153254}
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