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Simplifying a2 + -10a + 1 = 0 Reorder the terms: 1 + -10a + a2 = 0 Solving 1 + -10a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -10a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10a + a2 = 0 + -1 -10a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10a + a2 = -1 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 = -1 + 25 Reorder the terms: 25 + -10a + a2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + -10a + a2 = 24 Factor a perfect square on the left side: (a + -5)(a + -5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + -5) equal to 4.898979486 and -4.898979486.Subproblem 1
a + -5 = 4.898979486 Simplifying a + -5 = 4.898979486 Reorder the terms: -5 + a = 4.898979486 Solving -5 + a = 4.898979486 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 = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + a = 4.898979486 + 5 a = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 a = 9.898979486 Simplifying a = 9.898979486Subproblem 2
a + -5 = -4.898979486 Simplifying a + -5 = -4.898979486 Reorder the terms: -5 + a = -4.898979486 Solving -5 + a = -4.898979486 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 = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + a = -4.898979486 + 5 a = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 a = 0.101020514 Simplifying a = 0.101020514Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.898979486, 0.101020514}
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