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Simplifying 10a2 + 20a + -76 = 0 Reorder the terms: -76 + 20a + 10a2 = 0 Solving -76 + 20a + 10a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + 10a + 5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + 10a + 5a2)' equal to zero and attempt to solve: Simplifying -38 + 10a + 5a2 = 0 Solving -38 + 10a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + 2a + a2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + 2a + 7.6 + a2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + 2a + a2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + 2a + a2 = 0 + 7.6 2a + a2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 2a + a2 = 7.6 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 = 7.6 + 1 Reorder the terms: 1 + 2a + a2 = 7.6 + 1 Combine like terms: 7.6 + 1 = 8.6 1 + 2a + a2 = 8.6 Factor a perfect square on the left side: (a + 1)(a + 1) = 8.6 Calculate the square root of the right side: 2.93257566 Break this problem into two subproblems by setting (a + 1) equal to 2.93257566 and -2.93257566.Subproblem 1
a + 1 = 2.93257566 Simplifying a + 1 = 2.93257566 Reorder the terms: 1 + a = 2.93257566 Solving 1 + a = 2.93257566 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 = 2.93257566 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.93257566 + -1 a = 2.93257566 + -1 Combine like terms: 2.93257566 + -1 = 1.93257566 a = 1.93257566 Simplifying a = 1.93257566Subproblem 2
a + 1 = -2.93257566 Simplifying a + 1 = -2.93257566 Reorder the terms: 1 + a = -2.93257566 Solving 1 + a = -2.93257566 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 = -2.93257566 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.93257566 + -1 a = -2.93257566 + -1 Combine like terms: -2.93257566 + -1 = -3.93257566 a = -3.93257566 Simplifying a = -3.93257566Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.93257566, -3.93257566}Solution
a = {1.93257566, -3.93257566}
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