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Simplifying a2 + -10a = 100 Reorder the terms: -10a + a2 = 100 Solving -10a + a2 = 100 Solving for variable 'a'. Reorder the terms: -100 + -10a + a2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -10a + 100 + a2 = 0 + 100 Reorder the terms: -100 + 100 + -10a + a2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -10a + a2 = 0 + 100 -10a + a2 = 0 + 100 Combine like terms: 0 + 100 = 100 -10a + a2 = 100 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = 100 + 25 Reorder the terms: 25 + -10a + a2 = 100 + 25 Combine like terms: 100 + 25 = 125 25 + -10a + a2 = 125 Factor a perfect square on the left side: (a + -5)(a + -5) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (a + -5) equal to 11.180339887 and -11.180339887.Subproblem 1
a + -5 = 11.180339887 Simplifying a + -5 = 11.180339887 Reorder the terms: -5 + a = 11.180339887 Solving -5 + a = 11.180339887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + a = 11.180339887 + 5 a = 11.180339887 + 5 Combine like terms: 11.180339887 + 5 = 16.180339887 a = 16.180339887 Simplifying a = 16.180339887Subproblem 2
a + -5 = -11.180339887 Simplifying a + -5 = -11.180339887 Reorder the terms: -5 + a = -11.180339887 Solving -5 + a = -11.180339887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + a = -11.180339887 + 5 a = -11.180339887 + 5 Combine like terms: -11.180339887 + 5 = -6.180339887 a = -6.180339887 Simplifying a = -6.180339887Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.180339887, -6.180339887}
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