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Simplifying 100 = 10a2 + -32a + 26 Reorder the terms: 100 = 26 + -32a + 10a2 Solving 100 = 26 + -32a + 10a2 Solving for variable 'a'. Combine like terms: 100 + -26 = 74 74 + 32a + -10a2 = 26 + -32a + 10a2 + -26 + 32a + -10a2 Reorder the terms: 74 + 32a + -10a2 = 26 + -26 + -32a + 32a + 10a2 + -10a2 Combine like terms: 26 + -26 = 0 74 + 32a + -10a2 = 0 + -32a + 32a + 10a2 + -10a2 74 + 32a + -10a2 = -32a + 32a + 10a2 + -10a2 Combine like terms: -32a + 32a = 0 74 + 32a + -10a2 = 0 + 10a2 + -10a2 74 + 32a + -10a2 = 10a2 + -10a2 Combine like terms: 10a2 + -10a2 = 0 74 + 32a + -10a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(37 + 16a + -5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + 16a + -5a2)' equal to zero and attempt to solve: Simplifying 37 + 16a + -5a2 = 0 Solving 37 + 16a + -5a2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -7.4 + -3.2a + a2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + -3.2a + 7.4 + a2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + -3.2a + a2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + -3.2a + a2 = 0 + 7.4 -3.2a + a2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 -3.2a + a2 = 7.4 The a term is -3.2a. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2a + 2.56 + a2 = 7.4 + 2.56 Reorder the terms: 2.56 + -3.2a + a2 = 7.4 + 2.56 Combine like terms: 7.4 + 2.56 = 9.96 2.56 + -3.2a + a2 = 9.96 Factor a perfect square on the left side: (a + -1.6)(a + -1.6) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (a + -1.6) equal to 3.155946768 and -3.155946768.Subproblem 1
a + -1.6 = 3.155946768 Simplifying a + -1.6 = 3.155946768 Reorder the terms: -1.6 + a = 3.155946768 Solving -1.6 + a = 3.155946768 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = 3.155946768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = 3.155946768 + 1.6 a = 3.155946768 + 1.6 Combine like terms: 3.155946768 + 1.6 = 4.755946768 a = 4.755946768 Simplifying a = 4.755946768Subproblem 2
a + -1.6 = -3.155946768 Simplifying a + -1.6 = -3.155946768 Reorder the terms: -1.6 + a = -3.155946768 Solving -1.6 + a = -3.155946768 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = -3.155946768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = -3.155946768 + 1.6 a = -3.155946768 + 1.6 Combine like terms: -3.155946768 + 1.6 = -1.555946768 a = -1.555946768 Simplifying a = -1.555946768Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.755946768, -1.555946768}Solution
a = {4.755946768, -1.555946768}
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