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Simplifying -8a + 2a2 + -5 + 9a2 = 0 Reorder the terms: -5 + -8a + 2a2 + 9a2 = 0 Combine like terms: 2a2 + 9a2 = 11a2 -5 + -8a + 11a2 = 0 Solving -5 + -8a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + -0.7272727273a + a2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.7272727273a + 0.4545454545 + a2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.7272727273a + a2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.7272727273a + a2 = 0 + 0.4545454545 -0.7272727273a + a2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.7272727273a + a2 = 0.4545454545 The a term is -0.7272727273a. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273a + 0.1322314050 + a2 = 0.4545454545 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273a + a2 = 0.4545454545 + 0.1322314050 Combine like terms: 0.4545454545 + 0.1322314050 = 0.5867768595 0.1322314050 + -0.7272727273a + a2 = 0.5867768595 Factor a perfect square on the left side: (a + -0.3636363637)(a + -0.3636363637) = 0.5867768595 Calculate the square root of the right side: 0.766013616 Break this problem into two subproblems by setting (a + -0.3636363637) equal to 0.766013616 and -0.766013616.Subproblem 1
a + -0.3636363637 = 0.766013616 Simplifying a + -0.3636363637 = 0.766013616 Reorder the terms: -0.3636363637 + a = 0.766013616 Solving -0.3636363637 + a = 0.766013616 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + a = 0.766013616 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + a = 0.766013616 + 0.3636363637 a = 0.766013616 + 0.3636363637 Combine like terms: 0.766013616 + 0.3636363637 = 1.1296499797 a = 1.1296499797 Simplifying a = 1.1296499797Subproblem 2
a + -0.3636363637 = -0.766013616 Simplifying a + -0.3636363637 = -0.766013616 Reorder the terms: -0.3636363637 + a = -0.766013616 Solving -0.3636363637 + a = -0.766013616 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + a = -0.766013616 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + a = -0.766013616 + 0.3636363637 a = -0.766013616 + 0.3636363637 Combine like terms: -0.766013616 + 0.3636363637 = -0.4023772523 a = -0.4023772523 Simplifying a = -0.4023772523Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.1296499797, -0.4023772523}
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