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Simplifying 2a + 3a(a + -7) = a + 3 Reorder the terms: 2a + 3a(-7 + a) = a + 3 2a + (-7 * 3a + a * 3a) = a + 3 2a + (-21a + 3a2) = a + 3 Combine like terms: 2a + -21a = -19a -19a + 3a2 = a + 3 Reorder the terms: -19a + 3a2 = 3 + a Solving -19a + 3a2 = 3 + a Solving for variable 'a'. Reorder the terms: -3 + -19a + -1a + 3a2 = 3 + a + -3 + -1a Combine like terms: -19a + -1a = -20a -3 + -20a + 3a2 = 3 + a + -3 + -1a Reorder the terms: -3 + -20a + 3a2 = 3 + -3 + a + -1a Combine like terms: 3 + -3 = 0 -3 + -20a + 3a2 = 0 + a + -1a -3 + -20a + 3a2 = a + -1a Combine like terms: a + -1a = 0 -3 + -20a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -6.666666667a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.666666667a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -6.666666667a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.666666667a + a2 = 0 + 1 -6.666666667a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.666666667a + a2 = 1 The a term is -6.666666667a. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667a + 11.11111112 + a2 = 1 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667a + a2 = 1 + 11.11111112 Combine like terms: 1 + 11.11111112 = 12.11111112 11.11111112 + -6.666666667a + a2 = 12.11111112 Factor a perfect square on the left side: (a + -3.333333334)(a + -3.333333334) = 12.11111112 Calculate the square root of the right side: 3.480102171 Break this problem into two subproblems by setting (a + -3.333333334) equal to 3.480102171 and -3.480102171.Subproblem 1
a + -3.333333334 = 3.480102171 Simplifying a + -3.333333334 = 3.480102171 Reorder the terms: -3.333333334 + a = 3.480102171 Solving -3.333333334 + a = 3.480102171 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + a = 3.480102171 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + a = 3.480102171 + 3.333333334 a = 3.480102171 + 3.333333334 Combine like terms: 3.480102171 + 3.333333334 = 6.813435505 a = 6.813435505 Simplifying a = 6.813435505Subproblem 2
a + -3.333333334 = -3.480102171 Simplifying a + -3.333333334 = -3.480102171 Reorder the terms: -3.333333334 + a = -3.480102171 Solving -3.333333334 + a = -3.480102171 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + a = -3.480102171 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + a = -3.480102171 + 3.333333334 a = -3.480102171 + 3.333333334 Combine like terms: -3.480102171 + 3.333333334 = -0.146768837 a = -0.146768837 Simplifying a = -0.146768837Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.813435505, -0.146768837}
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