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Simplifying -50 = -3a(a + 3) Reorder the terms: -50 = -3a(3 + a) -50 = (3 * -3a + a * -3a) -50 = (-9a + -3a2) Solving -50 = -9a + -3a2 Solving for variable 'a'. Reorder the terms: -50 + 9a + 3a2 = -9a + 9a + -3a2 + 3a2 Combine like terms: -9a + 9a = 0 -50 + 9a + 3a2 = 0 + -3a2 + 3a2 -50 + 9a + 3a2 = -3a2 + 3a2 Combine like terms: -3a2 + 3a2 = 0 -50 + 9a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + 3a + a2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + 3a + 16.66666667 + a2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + 3a + a2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + 3a + a2 = 0 + 16.66666667 3a + a2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 3a + a2 = 16.66666667 The a term is 3a. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3a + 2.25 + a2 = 16.66666667 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 16.66666667 + 2.25 Combine like terms: 16.66666667 + 2.25 = 18.91666667 2.25 + 3a + a2 = 18.91666667 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 18.91666667 Calculate the square root of the right side: 4.349329451 Break this problem into two subproblems by setting (a + 1.5) equal to 4.349329451 and -4.349329451.Subproblem 1
a + 1.5 = 4.349329451 Simplifying a + 1.5 = 4.349329451 Reorder the terms: 1.5 + a = 4.349329451 Solving 1.5 + a = 4.349329451 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 4.349329451 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 4.349329451 + -1.5 a = 4.349329451 + -1.5 Combine like terms: 4.349329451 + -1.5 = 2.849329451 a = 2.849329451 Simplifying a = 2.849329451Subproblem 2
a + 1.5 = -4.349329451 Simplifying a + 1.5 = -4.349329451 Reorder the terms: 1.5 + a = -4.349329451 Solving 1.5 + a = -4.349329451 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -4.349329451 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -4.349329451 + -1.5 a = -4.349329451 + -1.5 Combine like terms: -4.349329451 + -1.5 = -5.849329451 a = -5.849329451 Simplifying a = -5.849329451Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.849329451, -5.849329451}
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