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Simplifying 5(4a)(4a) + 7(4a) + -9 = 0 Remove parenthesis around (4a) 5 * 4a(4a) + 7(4a) + -9 = 0 Remove parenthesis around (4a) 5 * 4a * 4a + 7(4a) + -9 = 0 Reorder the terms for easier multiplication: 5 * 4 * 4a * a + 7(4a) + -9 = 0 Multiply 5 * 4 20 * 4a * a + 7(4a) + -9 = 0 Multiply 20 * 4 80a * a + 7(4a) + -9 = 0 Multiply a * a 80a2 + 7(4a) + -9 = 0 Remove parenthesis around (4a) 80a2 + 7 * 4a + -9 = 0 Multiply 7 * 4 80a2 + 28a + -9 = 0 Reorder the terms: -9 + 28a + 80a2 = 0 Solving -9 + 28a + 80a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -0.1125 + 0.35a + a2 = 0.0 Move the constant term to the right: Add '0.1125' to each side of the equation. -0.1125 + 0.35a + 0.1125 + a2 = 0.0 + 0.1125 Reorder the terms: -0.1125 + 0.1125 + 0.35a + a2 = 0.0 + 0.1125 Combine like terms: -0.1125 + 0.1125 = 0.0000 0.0000 + 0.35a + a2 = 0.0 + 0.1125 0.35a + a2 = 0.0 + 0.1125 Combine like terms: 0.0 + 0.1125 = 0.1125 0.35a + a2 = 0.1125 The a term is 0.35a. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35a + 0.030625 + a2 = 0.1125 + 0.030625 Reorder the terms: 0.030625 + 0.35a + a2 = 0.1125 + 0.030625 Combine like terms: 0.1125 + 0.030625 = 0.143125 0.030625 + 0.35a + a2 = 0.143125 Factor a perfect square on the left side: (a + 0.175)(a + 0.175) = 0.143125 Calculate the square root of the right side: 0.378318649 Break this problem into two subproblems by setting (a + 0.175) equal to 0.378318649 and -0.378318649.Subproblem 1
a + 0.175 = 0.378318649 Simplifying a + 0.175 = 0.378318649 Reorder the terms: 0.175 + a = 0.378318649 Solving 0.175 + a = 0.378318649 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + a = 0.378318649 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + a = 0.378318649 + -0.175 a = 0.378318649 + -0.175 Combine like terms: 0.378318649 + -0.175 = 0.203318649 a = 0.203318649 Simplifying a = 0.203318649Subproblem 2
a + 0.175 = -0.378318649 Simplifying a + 0.175 = -0.378318649 Reorder the terms: 0.175 + a = -0.378318649 Solving 0.175 + a = -0.378318649 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + a = -0.378318649 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + a = -0.378318649 + -0.175 a = -0.378318649 + -0.175 Combine like terms: -0.378318649 + -0.175 = -0.553318649 a = -0.553318649 Simplifying a = -0.553318649Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.203318649, -0.553318649}
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