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Simplifying 7a(6 + -2a + -1a2) = 0 (6 * 7a + -2a * 7a + -1a2 * 7a) = 0 (42a + -14a2 + -7a3) = 0 Solving 42a + -14a2 + -7a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '7a'. 7a(6 + -2a + -1a2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(6 + -2a + -1a2)' equal to zero and attempt to solve: Simplifying 6 + -2a + -1a2 = 0 Solving 6 + -2a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 2a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + 2a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2a + a2 = 0 + 6 2a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 2a + a2 = 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 = 6 + 1 Reorder the terms: 1 + 2a + a2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2a + a2 = 7 Factor a perfect square on the left side: (a + 1)(a + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (a + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
a + 1 = 2.645751311 Simplifying a + 1 = 2.645751311 Reorder the terms: 1 + a = 2.645751311 Solving 1 + a = 2.645751311 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 = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.645751311 + -1 a = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 a = 1.645751311 Simplifying a = 1.645751311Subproblem 2
a + 1 = -2.645751311 Simplifying a + 1 = -2.645751311 Reorder the terms: 1 + a = -2.645751311 Solving 1 + a = -2.645751311 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 = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.645751311 + -1 a = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 a = -3.645751311 Simplifying a = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.645751311, -3.645751311}Solution
a = {0, 1.645751311, -3.645751311}
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