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Simplifying 2a2 + 20a = -2 Reorder the terms: 20a + 2a2 = -2 Solving 20a + 2a2 = -2 Solving for variable 'a'. Reorder the terms: 2 + 20a + 2a2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 20a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 10a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 10a + a2)' equal to zero and attempt to solve: Simplifying 1 + 10a + a2 = 0 Solving 1 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 10a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 10a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 10a + a2 = 0 + -1 10a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 10a + a2 = -1 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = -1 + 25 Reorder the terms: 25 + 10a + a2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + 10a + a2 = 24 Factor a perfect square on the left side: (a + 5)(a + 5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + 5) equal to 4.898979486 and -4.898979486.Subproblem 1
a + 5 = 4.898979486 Simplifying a + 5 = 4.898979486 Reorder the terms: 5 + a = 4.898979486 Solving 5 + a = 4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.898979486 + -5 a = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 a = -0.101020514 Simplifying a = -0.101020514Subproblem 2
a + 5 = -4.898979486 Simplifying a + 5 = -4.898979486 Reorder the terms: 5 + a = -4.898979486 Solving 5 + a = -4.898979486 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.898979486 + -5 a = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 a = -9.898979486 Simplifying a = -9.898979486Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.101020514, -9.898979486}Solution
a = {-0.101020514, -9.898979486}
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