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Simplifying -1(a2 + -2) = (a + -2) Reorder the terms: -1(-2 + a2) = (a + -2) (-2 * -1 + a2 * -1) = (a + -2) (2 + -1a2) = (a + -2) Reorder the terms: 2 + -1a2 = (-2 + a) Remove parenthesis around (-2 + a) 2 + -1a2 = -2 + a Solving 2 + -1a2 = -2 + a Solving for variable 'a'. Reorder the terms: 2 + 2 + -1a + -1a2 = -2 + a + 2 + -1a Combine like terms: 2 + 2 = 4 4 + -1a + -1a2 = -2 + a + 2 + -1a Reorder the terms: 4 + -1a + -1a2 = -2 + 2 + a + -1a Combine like terms: -2 + 2 = 0 4 + -1a + -1a2 = 0 + a + -1a 4 + -1a + -1a2 = a + -1a Combine like terms: a + -1a = 0 4 + -1a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + a + a2 = 0 + 4 a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 a + a2 = 4 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 1.25 + a2 = 4.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (a + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
a + 0.5 = 2.061552813 Simplifying a + 0.5 = 2.061552813 Reorder the terms: 0.5 + a = 2.061552813 Solving 0.5 + a = 2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2.061552813 + -0.5 a = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 a = 1.561552813 Simplifying a = 1.561552813Subproblem 2
a + 0.5 = -2.061552813 Simplifying a + 0.5 = -2.061552813 Reorder the terms: 0.5 + a = -2.061552813 Solving 0.5 + a = -2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2.061552813 + -0.5 a = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 a = -2.561552813 Simplifying a = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.561552813, -2.561552813}
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