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Simplifying 9a2 + 42a + -49 = 0 Reorder the terms: -49 + 42a + 9a2 = 0 Solving -49 + 42a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.444444444 + 4.666666667a + a2 = 0 Move the constant term to the right: Add '5.444444444' to each side of the equation. -5.444444444 + 4.666666667a + 5.444444444 + a2 = 0 + 5.444444444 Reorder the terms: -5.444444444 + 5.444444444 + 4.666666667a + a2 = 0 + 5.444444444 Combine like terms: -5.444444444 + 5.444444444 = 0.000000000 0.000000000 + 4.666666667a + a2 = 0 + 5.444444444 4.666666667a + a2 = 0 + 5.444444444 Combine like terms: 0 + 5.444444444 = 5.444444444 4.666666667a + a2 = 5.444444444 The a term is 4.666666667a. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667a + 5.444444448 + a2 = 5.444444444 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667a + a2 = 5.444444444 + 5.444444448 Combine like terms: 5.444444444 + 5.444444448 = 10.888888892 5.444444448 + 4.666666667a + a2 = 10.888888892 Factor a perfect square on the left side: (a + 2.333333334)(a + 2.333333334) = 10.888888892 Calculate the square root of the right side: 3.299831646 Break this problem into two subproblems by setting (a + 2.333333334) equal to 3.299831646 and -3.299831646.Subproblem 1
a + 2.333333334 = 3.299831646 Simplifying a + 2.333333334 = 3.299831646 Reorder the terms: 2.333333334 + a = 3.299831646 Solving 2.333333334 + a = 3.299831646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + a = 3.299831646 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + a = 3.299831646 + -2.333333334 a = 3.299831646 + -2.333333334 Combine like terms: 3.299831646 + -2.333333334 = 0.966498312 a = 0.966498312 Simplifying a = 0.966498312Subproblem 2
a + 2.333333334 = -3.299831646 Simplifying a + 2.333333334 = -3.299831646 Reorder the terms: 2.333333334 + a = -3.299831646 Solving 2.333333334 + a = -3.299831646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + a = -3.299831646 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + a = -3.299831646 + -2.333333334 a = -3.299831646 + -2.333333334 Combine like terms: -3.299831646 + -2.333333334 = -5.63316498 a = -5.63316498 Simplifying a = -5.63316498Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.966498312, -5.63316498}
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