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Simplifying 2a2 + -1a + -13 = 12 Reorder the terms: -13 + -1a + 2a2 = 12 Solving -13 + -1a + 2a2 = 12 Solving for variable 'a'. Reorder the terms: -13 + -12 + -1a + 2a2 = 12 + -12 Combine like terms: -13 + -12 = -25 -25 + -1a + 2a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -25 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -0.5a + a2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.5a + 12.5 + a2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.5a + a2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.5a + a2 = 0 + 12.5 -0.5a + a2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.5a + a2 = 12.5 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 12.5 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 12.5 + 0.0625 Combine like terms: 12.5 + 0.0625 = 12.5625 0.0625 + -0.5a + a2 = 12.5625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (a + -0.25) equal to 3.54436172 and -3.54436172.Subproblem 1
a + -0.25 = 3.54436172 Simplifying a + -0.25 = 3.54436172 Reorder the terms: -0.25 + a = 3.54436172 Solving -0.25 + a = 3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 3.54436172 + 0.25 a = 3.54436172 + 0.25 Combine like terms: 3.54436172 + 0.25 = 3.79436172 a = 3.79436172 Simplifying a = 3.79436172Subproblem 2
a + -0.25 = -3.54436172 Simplifying a + -0.25 = -3.54436172 Reorder the terms: -0.25 + a = -3.54436172 Solving -0.25 + a = -3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -3.54436172 + 0.25 a = -3.54436172 + 0.25 Combine like terms: -3.54436172 + 0.25 = -3.29436172 a = -3.29436172 Simplifying a = -3.29436172Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.79436172, -3.29436172}
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