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Simplifying 64a2 + -22 = -10a Reorder the terms: -22 + 64a2 = -10a Solving -22 + 64a2 = -10a Solving for variable 'a'. Reorder the terms: -22 + 10a + 64a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -22 + 10a + 64a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 5a + 32a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 5a + 32a2)' equal to zero and attempt to solve: Simplifying -11 + 5a + 32a2 = 0 Solving -11 + 5a + 32a2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.34375 + 0.15625a + a2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + 0.15625a + 0.34375 + a2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + 0.15625a + a2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + 0.15625a + a2 = 0 + 0.34375 0.15625a + a2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 0.15625a + a2 = 0.34375 The a term is 0.15625a. Take half its coefficient (0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. 0.15625a + 0.006103515625 + a2 = 0.34375 + 0.006103515625 Reorder the terms: 0.006103515625 + 0.15625a + a2 = 0.34375 + 0.006103515625 Combine like terms: 0.34375 + 0.006103515625 = 0.349853515625 0.006103515625 + 0.15625a + a2 = 0.349853515625 Factor a perfect square on the left side: (a + 0.078125)(a + 0.078125) = 0.349853515625 Calculate the square root of the right side: 0.591484163 Break this problem into two subproblems by setting (a + 0.078125) equal to 0.591484163 and -0.591484163.Subproblem 1
a + 0.078125 = 0.591484163 Simplifying a + 0.078125 = 0.591484163 Reorder the terms: 0.078125 + a = 0.591484163 Solving 0.078125 + a = 0.591484163 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + a = 0.591484163 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + a = 0.591484163 + -0.078125 a = 0.591484163 + -0.078125 Combine like terms: 0.591484163 + -0.078125 = 0.513359163 a = 0.513359163 Simplifying a = 0.513359163Subproblem 2
a + 0.078125 = -0.591484163 Simplifying a + 0.078125 = -0.591484163 Reorder the terms: 0.078125 + a = -0.591484163 Solving 0.078125 + a = -0.591484163 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.078125' to each side of the equation. 0.078125 + -0.078125 + a = -0.591484163 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + a = -0.591484163 + -0.078125 a = -0.591484163 + -0.078125 Combine like terms: -0.591484163 + -0.078125 = -0.669609163 a = -0.669609163 Simplifying a = -0.669609163Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.513359163, -0.669609163}Solution
a = {0.513359163, -0.669609163}
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