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Simplifying 40a2b + 12ab + -49b = 0 Reorder the terms: 12ab + 40a2b + -49b = 0 Solving 12ab + 40a2b + -49b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'b'. b(12a + 40a2 + -49) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b = 0 + -1b Remove the zero: 0 = -1b Simplifying 0 = -1b The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(12a + 40a2 + -49)' equal to zero and attempt to solve: Simplifying 12a + 40a2 + -49 = 0 Reorder the terms: -49 + 12a + 40a2 = 0 Solving -49 + 12a + 40a2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -1.225 + 0.3a + a2 = 0 Move the constant term to the right: Add '1.225' to each side of the equation. -1.225 + 0.3a + 1.225 + a2 = 0 + 1.225 Reorder the terms: -1.225 + 1.225 + 0.3a + a2 = 0 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + 0.3a + a2 = 0 + 1.225 0.3a + a2 = 0 + 1.225 Combine like terms: 0 + 1.225 = 1.225 0.3a + a2 = 1.225 The a term is 0.3a. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3a + 0.0225 + a2 = 1.225 + 0.0225 Reorder the terms: 0.0225 + 0.3a + a2 = 1.225 + 0.0225 Combine like terms: 1.225 + 0.0225 = 1.2475 0.0225 + 0.3a + a2 = 1.2475 Factor a perfect square on the left side: (a + 0.15)(a + 0.15) = 1.2475 Calculate the square root of the right side: 1.116915395 Break this problem into two subproblems by setting (a + 0.15) equal to 1.116915395 and -1.116915395.Subproblem 1
a + 0.15 = 1.116915395 Simplifying a + 0.15 = 1.116915395 Reorder the terms: 0.15 + a = 1.116915395 Solving 0.15 + a = 1.116915395 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + a = 1.116915395 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + a = 1.116915395 + -0.15 a = 1.116915395 + -0.15 Combine like terms: 1.116915395 + -0.15 = 0.966915395 a = 0.966915395 Simplifying a = 0.966915395Subproblem 2
a + 0.15 = -1.116915395 Simplifying a + 0.15 = -1.116915395 Reorder the terms: 0.15 + a = -1.116915395 Solving 0.15 + a = -1.116915395 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + a = -1.116915395 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + a = -1.116915395 + -0.15 a = -1.116915395 + -0.15 Combine like terms: -1.116915395 + -0.15 = -1.266915395 a = -1.266915395 Simplifying a = -1.266915395Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.966915395, -1.266915395}Solution
a = {0.966915395, -1.266915395}
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