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Simplifying 2a2 + -20a + 7 = 0 Reorder the terms: 7 + -20a + 2a2 = 0 Solving 7 + -20a + 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'. 3.5 + -10a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -10a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -10a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -10a + a2 = 0 + -3.5 -10a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -10a + a2 = -3.5 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 = -3.5 + 25 Reorder the terms: 25 + -10a + a2 = -3.5 + 25 Combine like terms: -3.5 + 25 = 21.5 25 + -10a + a2 = 21.5 Factor a perfect square on the left side: (a + -5)(a + -5) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (a + -5) equal to 4.636809248 and -4.636809248.Subproblem 1
a + -5 = 4.636809248 Simplifying a + -5 = 4.636809248 Reorder the terms: -5 + a = 4.636809248 Solving -5 + a = 4.636809248 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 = 4.636809248 + 5 Combine like terms: -5 + 5 = 0 0 + a = 4.636809248 + 5 a = 4.636809248 + 5 Combine like terms: 4.636809248 + 5 = 9.636809248 a = 9.636809248 Simplifying a = 9.636809248Subproblem 2
a + -5 = -4.636809248 Simplifying a + -5 = -4.636809248 Reorder the terms: -5 + a = -4.636809248 Solving -5 + a = -4.636809248 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 = -4.636809248 + 5 Combine like terms: -5 + 5 = 0 0 + a = -4.636809248 + 5 a = -4.636809248 + 5 Combine like terms: -4.636809248 + 5 = 0.363190752 a = 0.363190752 Simplifying a = 0.363190752Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.636809248, 0.363190752}
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