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Simplifying 4(2a + -1) = -10a(a + -5) Reorder the terms: 4(-1 + 2a) = -10a(a + -5) (-1 * 4 + 2a * 4) = -10a(a + -5) (-4 + 8a) = -10a(a + -5) Reorder the terms: -4 + 8a = -10a(-5 + a) -4 + 8a = (-5 * -10a + a * -10a) -4 + 8a = (50a + -10a2) Solving -4 + 8a = 50a + -10a2 Solving for variable 'a'. Combine like terms: 8a + -50a = -42a -4 + -42a + 10a2 = 50a + -10a2 + -50a + 10a2 Reorder the terms: -4 + -42a + 10a2 = 50a + -50a + -10a2 + 10a2 Combine like terms: 50a + -50a = 0 -4 + -42a + 10a2 = 0 + -10a2 + 10a2 -4 + -42a + 10a2 = -10a2 + 10a2 Combine like terms: -10a2 + 10a2 = 0 -4 + -42a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -21a + 5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -21a + 5a2)' equal to zero and attempt to solve: Simplifying -2 + -21a + 5a2 = 0 Solving -2 + -21a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -4.2a + a2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -4.2a + 0.4 + a2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -4.2a + a2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -4.2a + a2 = 0 + 0.4 -4.2a + a2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -4.2a + a2 = 0.4 The a term is -4.2a. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2a + 4.41 + a2 = 0.4 + 4.41 Reorder the terms: 4.41 + -4.2a + a2 = 0.4 + 4.41 Combine like terms: 0.4 + 4.41 = 4.81 4.41 + -4.2a + a2 = 4.81 Factor a perfect square on the left side: (a + -2.1)(a + -2.1) = 4.81 Calculate the square root of the right side: 2.19317122 Break this problem into two subproblems by setting (a + -2.1) equal to 2.19317122 and -2.19317122.Subproblem 1
a + -2.1 = 2.19317122 Simplifying a + -2.1 = 2.19317122 Reorder the terms: -2.1 + a = 2.19317122 Solving -2.1 + a = 2.19317122 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + a = 2.19317122 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + a = 2.19317122 + 2.1 a = 2.19317122 + 2.1 Combine like terms: 2.19317122 + 2.1 = 4.29317122 a = 4.29317122 Simplifying a = 4.29317122Subproblem 2
a + -2.1 = -2.19317122 Simplifying a + -2.1 = -2.19317122 Reorder the terms: -2.1 + a = -2.19317122 Solving -2.1 + a = -2.19317122 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + a = -2.19317122 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + a = -2.19317122 + 2.1 a = -2.19317122 + 2.1 Combine like terms: -2.19317122 + 2.1 = -0.09317122 a = -0.09317122 Simplifying a = -0.09317122Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.29317122, -0.09317122}Solution
a = {4.29317122, -0.09317122}
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