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Simplifying 3a2 + -26a + 9 = 0 Reorder the terms: 9 + -26a + 3a2 = 0 Solving 9 + -26a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + -8.666666667a + a2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8.666666667a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + -8.666666667a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8.666666667a + a2 = 0 + -3 -8.666666667a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8.666666667a + a2 = -3 The a term is -8.666666667a. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667a + 18.77777778 + a2 = -3 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667a + a2 = -3 + 18.77777778 Combine like terms: -3 + 18.77777778 = 15.77777778 18.77777778 + -8.666666667a + a2 = 15.77777778 Factor a perfect square on the left side: (a + -4.333333334)(a + -4.333333334) = 15.77777778 Calculate the square root of the right side: 3.972125096 Break this problem into two subproblems by setting (a + -4.333333334) equal to 3.972125096 and -3.972125096.Subproblem 1
a + -4.333333334 = 3.972125096 Simplifying a + -4.333333334 = 3.972125096 Reorder the terms: -4.333333334 + a = 3.972125096 Solving -4.333333334 + a = 3.972125096 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + a = 3.972125096 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + a = 3.972125096 + 4.333333334 a = 3.972125096 + 4.333333334 Combine like terms: 3.972125096 + 4.333333334 = 8.30545843 a = 8.30545843 Simplifying a = 8.30545843Subproblem 2
a + -4.333333334 = -3.972125096 Simplifying a + -4.333333334 = -3.972125096 Reorder the terms: -4.333333334 + a = -3.972125096 Solving -4.333333334 + a = -3.972125096 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + a = -3.972125096 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + a = -3.972125096 + 4.333333334 a = -3.972125096 + 4.333333334 Combine like terms: -3.972125096 + 4.333333334 = 0.361208238 a = 0.361208238 Simplifying a = 0.361208238Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.30545843, 0.361208238}
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