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Simplifying 4a + -9a2 + 1 + -4a2 = 0 Reorder the terms: 1 + 4a + -9a2 + -4a2 = 0 Combine like terms: -9a2 + -4a2 = -13a2 1 + 4a + -13a2 = 0 Solving 1 + 4a + -13a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.07692307692 + -0.3076923077a + a2 = 0 Move the constant term to the right: Add '0.07692307692' to each side of the equation. -0.07692307692 + -0.3076923077a + 0.07692307692 + a2 = 0 + 0.07692307692 Reorder the terms: -0.07692307692 + 0.07692307692 + -0.3076923077a + a2 = 0 + 0.07692307692 Combine like terms: -0.07692307692 + 0.07692307692 = 0.00000000000 0.00000000000 + -0.3076923077a + a2 = 0 + 0.07692307692 -0.3076923077a + a2 = 0 + 0.07692307692 Combine like terms: 0 + 0.07692307692 = 0.07692307692 -0.3076923077a + a2 = 0.07692307692 The a term is -0.3076923077a. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077a + 0.02366863907 + a2 = 0.07692307692 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077a + a2 = 0.07692307692 + 0.02366863907 Combine like terms: 0.07692307692 + 0.02366863907 = 0.10059171599 0.02366863907 + -0.3076923077a + a2 = 0.10059171599 Factor a perfect square on the left side: (a + -0.1538461539)(a + -0.1538461539) = 0.10059171599 Calculate the square root of the right side: 0.317161971 Break this problem into two subproblems by setting (a + -0.1538461539) equal to 0.317161971 and -0.317161971.Subproblem 1
a + -0.1538461539 = 0.317161971 Simplifying a + -0.1538461539 = 0.317161971 Reorder the terms: -0.1538461539 + a = 0.317161971 Solving -0.1538461539 + a = 0.317161971 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + a = 0.317161971 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + a = 0.317161971 + 0.1538461539 a = 0.317161971 + 0.1538461539 Combine like terms: 0.317161971 + 0.1538461539 = 0.4710081249 a = 0.4710081249 Simplifying a = 0.4710081249Subproblem 2
a + -0.1538461539 = -0.317161971 Simplifying a + -0.1538461539 = -0.317161971 Reorder the terms: -0.1538461539 + a = -0.317161971 Solving -0.1538461539 + a = -0.317161971 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + a = -0.317161971 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + a = -0.317161971 + 0.1538461539 a = -0.317161971 + 0.1538461539 Combine like terms: -0.317161971 + 0.1538461539 = -0.1633158171 a = -0.1633158171 Simplifying a = -0.1633158171Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.4710081249, -0.1633158171}
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