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Simplifying 4a2 + 10a = 12 Reorder the terms: 10a + 4a2 = 12 Solving 10a + 4a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + 10a + 4a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 10a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 5a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 5a + 2a2)' equal to zero and attempt to solve: Simplifying -6 + 5a + 2a2 = 0 Solving -6 + 5a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 2.5a + a2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.5a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 2.5a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.5a + a2 = 0 + 3 2.5a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.5a + a2 = 3 The a term is 2.5a. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5a + 1.5625 + a2 = 3 + 1.5625 Reorder the terms: 1.5625 + 2.5a + a2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + 2.5a + a2 = 4.5625 Factor a perfect square on the left side: (a + 1.25)(a + 1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (a + 1.25) equal to 2.136000936 and -2.136000936.Subproblem 1
a + 1.25 = 2.136000936 Simplifying a + 1.25 = 2.136000936 Reorder the terms: 1.25 + a = 2.136000936 Solving 1.25 + a = 2.136000936 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = 2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = 2.136000936 + -1.25 a = 2.136000936 + -1.25 Combine like terms: 2.136000936 + -1.25 = 0.886000936 a = 0.886000936 Simplifying a = 0.886000936Subproblem 2
a + 1.25 = -2.136000936 Simplifying a + 1.25 = -2.136000936 Reorder the terms: 1.25 + a = -2.136000936 Solving 1.25 + a = -2.136000936 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = -2.136000936 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = -2.136000936 + -1.25 a = -2.136000936 + -1.25 Combine like terms: -2.136000936 + -1.25 = -3.386000936 a = -3.386000936 Simplifying a = -3.386000936Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.886000936, -3.386000936}Solution
a = {0.886000936, -3.386000936}
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