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Simplifying -3a2 + 26a + -3 = 0 Reorder the terms: -3 + 26a + -3a2 = 0 Solving -3 + 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'. 1 + -8.666666667a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8.666666667a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -8.666666667a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8.666666667a + a2 = 0 + -1 -8.666666667a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8.666666667a + a2 = -1 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 = -1 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667a + a2 = -1 + 18.77777778 Combine like terms: -1 + 18.77777778 = 17.77777778 18.77777778 + -8.666666667a + a2 = 17.77777778 Factor a perfect square on the left side: (a + -4.333333334)(a + -4.333333334) = 17.77777778 Calculate the square root of the right side: 4.216370214 Break this problem into two subproblems by setting (a + -4.333333334) equal to 4.216370214 and -4.216370214.Subproblem 1
a + -4.333333334 = 4.216370214 Simplifying a + -4.333333334 = 4.216370214 Reorder the terms: -4.333333334 + a = 4.216370214 Solving -4.333333334 + a = 4.216370214 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 = 4.216370214 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + a = 4.216370214 + 4.333333334 a = 4.216370214 + 4.333333334 Combine like terms: 4.216370214 + 4.333333334 = 8.549703548 a = 8.549703548 Simplifying a = 8.549703548Subproblem 2
a + -4.333333334 = -4.216370214 Simplifying a + -4.333333334 = -4.216370214 Reorder the terms: -4.333333334 + a = -4.216370214 Solving -4.333333334 + a = -4.216370214 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 = -4.216370214 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + a = -4.216370214 + 4.333333334 a = -4.216370214 + 4.333333334 Combine like terms: -4.216370214 + 4.333333334 = 0.11696312 a = 0.11696312 Simplifying a = 0.11696312Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.549703548, 0.11696312}
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