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Simplifying 4a + -66a * 65744(-555) * a = 16 Reorder the terms for easier multiplication: 4a + -66 * 65744 * -555a * a = 16 Multiply -66 * 65744 4a + -4339104 * -555a * a = 16 Multiply -4339104 * -555 4a + 2408202720a * a = 16 Multiply a * a 4a + 2408202720a2 = 16 Solving 4a + 2408202720a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + 4a + 2408202720a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 4a + 2408202720a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + a + 602050680a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + a + 602050680a2)' equal to zero and attempt to solve: Simplifying -4 + a + 602050680a2 = 0 Solving -4 + a + 602050680a2 = 0 Begin completing the square. Divide all terms by 602050680 the coefficient of the squared term: Divide each side by '602050680'. -0.000000006643958944 + 0.000000001660989736a + a2 = 0.0 Move the constant term to the right: Add '0.000000006643958944' to each side of the equation. -0.000000006643958944 + 0.000000001660989736a + 0.000000006643958944 + a2 = 0.0 + 0.000000006643958944 Reorder the terms: -0.000000006643958944 + 0.000000006643958944 + 0.000000001660989736a + a2 = 0.0 + 0.000000006643958944 Combine like terms: -0.000000006643958944 + 0.000000006643958944 = 0.000000000000000000 0.000000000000000000 + 0.000000001660989736a + a2 = 0.0 + 0.000000006643958944 0.000000001660989736a + a2 = 0.0 + 0.000000006643958944 Combine like terms: 0.0 + 0.000000006643958944 = 0.000000006643958944 0.000000001660989736a + a2 = 0.000000006643958944 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.000000001660989736a + 0.25 + a2 = 0.000000006643958944 + 0.25 Reorder the terms: 0.25 + 0.000000001660989736a + a2 = 0.000000006643958944 + 0.25 Combine like terms: 0.000000006643958944 + 0.25 = 0.250000006643958944 0.25 + 0.000000001660989736a + a2 = 0.250000006643958944 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.250000006643958944 Calculate the square root of the right side: 0.500000007 Break this problem into two subproblems by setting (a + 0.5) equal to 0.500000007 and -0.500000007.Subproblem 1
a + 0.5 = 0.500000007 Simplifying a + 0.5 = 0.500000007 Reorder the terms: 0.5 + a = 0.500000007 Solving 0.5 + a = 0.500000007 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.500000007 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.500000007 + -0.5 a = 0.500000007 + -0.5 Combine like terms: 0.500000007 + -0.5 = 0.000000007 a = 0.000000007 Simplifying a = 0.000000007Subproblem 2
a + 0.5 = -0.500000007 Simplifying a + 0.5 = -0.500000007 Reorder the terms: 0.5 + a = -0.500000007 Solving 0.5 + a = -0.500000007 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.500000007 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.500000007 + -0.5 a = -0.500000007 + -0.5 Combine like terms: -0.500000007 + -0.5 = -1.000000007 a = -1.000000007 Simplifying a = -1.000000007Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.000000007, -1.000000007}Solution
a = {0.000000007, -1.000000007}
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