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Simplifying a2 + 21a + -10 = 0 Reorder the terms: -10 + 21a + a2 = 0 Solving -10 + 21a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 21a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + 21a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 21a + a2 = 0 + 10 21a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 21a + a2 = 10 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 = 10 + 110.25 Reorder the terms: 110.25 + 21a + a2 = 10 + 110.25 Combine like terms: 10 + 110.25 = 120.25 110.25 + 21a + a2 = 120.25 Factor a perfect square on the left side: (a + 10.5)(a + 10.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (a + 10.5) equal to 10.9658561 and -10.9658561.Subproblem 1
a + 10.5 = 10.9658561 Simplifying a + 10.5 = 10.9658561 Reorder the terms: 10.5 + a = 10.9658561 Solving 10.5 + a = 10.9658561 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 = 10.9658561 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + a = 10.9658561 + -10.5 a = 10.9658561 + -10.5 Combine like terms: 10.9658561 + -10.5 = 0.4658561 a = 0.4658561 Simplifying a = 0.4658561Subproblem 2
a + 10.5 = -10.9658561 Simplifying a + 10.5 = -10.9658561 Reorder the terms: 10.5 + a = -10.9658561 Solving 10.5 + a = -10.9658561 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 = -10.9658561 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + a = -10.9658561 + -10.5 a = -10.9658561 + -10.5 Combine like terms: -10.9658561 + -10.5 = -21.4658561 a = -21.4658561 Simplifying a = -21.4658561Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.4658561, -21.4658561}
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