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Simplifying 2a2 + -46a + 225 = 0 Reorder the terms: 225 + -46a + 2a2 = 0 Solving 225 + -46a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 112.5 + -23a + a2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -23a + -112.5 + a2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -23a + a2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -23a + a2 = 0 + -112.5 -23a + a2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -23a + a2 = -112.5 The a term is -23a. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23a + 132.25 + a2 = -112.5 + 132.25 Reorder the terms: 132.25 + -23a + a2 = -112.5 + 132.25 Combine like terms: -112.5 + 132.25 = 19.75 132.25 + -23a + a2 = 19.75 Factor a perfect square on the left side: (a + -11.5)(a + -11.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (a + -11.5) equal to 4.444097209 and -4.444097209.Subproblem 1
a + -11.5 = 4.444097209 Simplifying a + -11.5 = 4.444097209 Reorder the terms: -11.5 + a = 4.444097209 Solving -11.5 + a = 4.444097209 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + a = 4.444097209 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + a = 4.444097209 + 11.5 a = 4.444097209 + 11.5 Combine like terms: 4.444097209 + 11.5 = 15.944097209 a = 15.944097209 Simplifying a = 15.944097209Subproblem 2
a + -11.5 = -4.444097209 Simplifying a + -11.5 = -4.444097209 Reorder the terms: -11.5 + a = -4.444097209 Solving -11.5 + a = -4.444097209 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + a = -4.444097209 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + a = -4.444097209 + 11.5 a = -4.444097209 + 11.5 Combine like terms: -4.444097209 + 11.5 = 7.055902791 a = 7.055902791 Simplifying a = 7.055902791Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.944097209, 7.055902791}
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