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Simplifying 7a2 + 32 = 776 + -515140a Reorder the terms: 32 + 7a2 = 776 + -515140a Solving 32 + 7a2 = 776 + -515140a Solving for variable 'a'. Reorder the terms: 32 + -776 + 515140a + 7a2 = 776 + -515140a + -776 + 515140a Combine like terms: 32 + -776 = -744 -744 + 515140a + 7a2 = 776 + -515140a + -776 + 515140a Reorder the terms: -744 + 515140a + 7a2 = 776 + -776 + -515140a + 515140a Combine like terms: 776 + -776 = 0 -744 + 515140a + 7a2 = 0 + -515140a + 515140a -744 + 515140a + 7a2 = -515140a + 515140a Combine like terms: -515140a + 515140a = 0 -744 + 515140a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -106.2857143 + 73591.42857a + a2 = 0 Move the constant term to the right: Add '106.2857143' to each side of the equation. -106.2857143 + 73591.42857a + 106.2857143 + a2 = 0 + 106.2857143 Reorder the terms: -106.2857143 + 106.2857143 + 73591.42857a + a2 = 0 + 106.2857143 Combine like terms: -106.2857143 + 106.2857143 = 0.0000000 0.0000000 + 73591.42857a + a2 = 0 + 106.2857143 73591.42857a + a2 = 0 + 106.2857143 Combine like terms: 0 + 106.2857143 = 106.2857143 73591.42857a + a2 = 106.2857143 The a term is 73591.42857a. Take half its coefficient (36795.71429). Square it (1353924590) and add it to both sides. Add '1353924590' to each side of the equation. 73591.42857a + 1353924590 + a2 = 106.2857143 + 1353924590 Reorder the terms: 1353924590 + 73591.42857a + a2 = 106.2857143 + 1353924590 Combine like terms: 106.2857143 + 1353924590 = 1353924696.2857143 1353924590 + 73591.42857a + a2 = 1353924696.2857143 Factor a perfect square on the left side: (a + 36795.71429)(a + 36795.71429) = 1353924696.2857143 Calculate the square root of the right side: 36795.715732755 Break this problem into two subproblems by setting (a + 36795.71429) equal to 36795.715732755 and -36795.715732755.Subproblem 1
a + 36795.71429 = 36795.715732755 Simplifying a + 36795.71429 = 36795.715732755 Reorder the terms: 36795.71429 + a = 36795.715732755 Solving 36795.71429 + a = 36795.715732755 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-36795.71429' to each side of the equation. 36795.71429 + -36795.71429 + a = 36795.715732755 + -36795.71429 Combine like terms: 36795.71429 + -36795.71429 = 0.00000 0.00000 + a = 36795.715732755 + -36795.71429 a = 36795.715732755 + -36795.71429 Combine like terms: 36795.715732755 + -36795.71429 = 0.001442755 a = 0.001442755 Simplifying a = 0.001442755Subproblem 2
a + 36795.71429 = -36795.715732755 Simplifying a + 36795.71429 = -36795.715732755 Reorder the terms: 36795.71429 + a = -36795.715732755 Solving 36795.71429 + a = -36795.715732755 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-36795.71429' to each side of the equation. 36795.71429 + -36795.71429 + a = -36795.715732755 + -36795.71429 Combine like terms: 36795.71429 + -36795.71429 = 0.00000 0.00000 + a = -36795.715732755 + -36795.71429 a = -36795.715732755 + -36795.71429 Combine like terms: -36795.715732755 + -36795.71429 = -73591.430022755 a = -73591.430022755 Simplifying a = -73591.430022755Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.001442755, -73591.430022755}
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