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Simplifying 4a2 + 8a + -20 = 0 Reorder the terms: -20 + 8a + 4a2 = 0 Solving -20 + 8a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 2a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 2a + a2)' equal to zero and attempt to solve: Simplifying -5 + 2a + a2 = 0 Solving -5 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + 2a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2a + a2 = 0 + 5 2a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 2a + a2 = 5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 5 + 1 Reorder the terms: 1 + 2a + a2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2a + a2 = 6 Factor a perfect square on the left side: (a + 1)(a + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
a + 1 = 2.449489743 Simplifying a + 1 = 2.449489743 Reorder the terms: 1 + a = 2.449489743 Solving 1 + a = 2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.449489743 + -1 a = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 a = 1.449489743 Simplifying a = 1.449489743Subproblem 2
a + 1 = -2.449489743 Simplifying a + 1 = -2.449489743 Reorder the terms: 1 + a = -2.449489743 Solving 1 + a = -2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.449489743 + -1 a = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 a = -3.449489743 Simplifying a = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.449489743, -3.449489743}Solution
a = {1.449489743, -3.449489743}
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