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Simplifying 0 = 10a2 + 475a + -2400 Reorder the terms: 0 = -2400 + 475a + 10a2 Solving 0 = -2400 + 475a + 10a2 Solving for variable 'a'. Combine like terms: 0 + 2400 = 2400 2400 + -475a + -10a2 = -2400 + 475a + 10a2 + 2400 + -475a + -10a2 Reorder the terms: 2400 + -475a + -10a2 = -2400 + 2400 + 475a + -475a + 10a2 + -10a2 Combine like terms: -2400 + 2400 = 0 2400 + -475a + -10a2 = 0 + 475a + -475a + 10a2 + -10a2 2400 + -475a + -10a2 = 475a + -475a + 10a2 + -10a2 Combine like terms: 475a + -475a = 0 2400 + -475a + -10a2 = 0 + 10a2 + -10a2 2400 + -475a + -10a2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 2400 + -475a + -10a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(480 + -95a + -2a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(480 + -95a + -2a2)' equal to zero and attempt to solve: Simplifying 480 + -95a + -2a2 = 0 Solving 480 + -95a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -240 + 47.5a + a2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 47.5a + 240 + a2 = 0 + 240 Reorder the terms: -240 + 240 + 47.5a + a2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 47.5a + a2 = 0 + 240 47.5a + a2 = 0 + 240 Combine like terms: 0 + 240 = 240 47.5a + a2 = 240 The a term is 47.5a. Take half its coefficient (23.75). Square it (564.0625) and add it to both sides. Add '564.0625' to each side of the equation. 47.5a + 564.0625 + a2 = 240 + 564.0625 Reorder the terms: 564.0625 + 47.5a + a2 = 240 + 564.0625 Combine like terms: 240 + 564.0625 = 804.0625 564.0625 + 47.5a + a2 = 804.0625 Factor a perfect square on the left side: (a + 23.75)(a + 23.75) = 804.0625 Calculate the square root of the right side: 28.355995839 Break this problem into two subproblems by setting (a + 23.75) equal to 28.355995839 and -28.355995839.Subproblem 1
a + 23.75 = 28.355995839 Simplifying a + 23.75 = 28.355995839 Reorder the terms: 23.75 + a = 28.355995839 Solving 23.75 + a = 28.355995839 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-23.75' to each side of the equation. 23.75 + -23.75 + a = 28.355995839 + -23.75 Combine like terms: 23.75 + -23.75 = 0.00 0.00 + a = 28.355995839 + -23.75 a = 28.355995839 + -23.75 Combine like terms: 28.355995839 + -23.75 = 4.605995839 a = 4.605995839 Simplifying a = 4.605995839Subproblem 2
a + 23.75 = -28.355995839 Simplifying a + 23.75 = -28.355995839 Reorder the terms: 23.75 + a = -28.355995839 Solving 23.75 + a = -28.355995839 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-23.75' to each side of the equation. 23.75 + -23.75 + a = -28.355995839 + -23.75 Combine like terms: 23.75 + -23.75 = 0.00 0.00 + a = -28.355995839 + -23.75 a = -28.355995839 + -23.75 Combine like terms: -28.355995839 + -23.75 = -52.105995839 a = -52.105995839 Simplifying a = -52.105995839Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.605995839, -52.105995839}Solution
a = {4.605995839, -52.105995839}
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