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Simplifying a2 + -10a + 14 = 0 Reorder the terms: 14 + -10a + a2 = 0 Solving 14 + -10a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10a + -14 + a2 = 0 + -14 Reorder the terms: 14 + -14 + -10a + a2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10a + a2 = 0 + -14 -10a + a2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10a + a2 = -14 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 = -14 + 25 Reorder the terms: 25 + -10a + a2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10a + a2 = 11 Factor a perfect square on the left side: (a + -5)(a + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (a + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
a + -5 = 3.31662479 Simplifying a + -5 = 3.31662479 Reorder the terms: -5 + a = 3.31662479 Solving -5 + a = 3.31662479 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 = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + a = 3.31662479 + 5 a = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 a = 8.31662479 Simplifying a = 8.31662479Subproblem 2
a + -5 = -3.31662479 Simplifying a + -5 = -3.31662479 Reorder the terms: -5 + a = -3.31662479 Solving -5 + a = -3.31662479 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 = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + a = -3.31662479 + 5 a = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 a = 1.68337521 Simplifying a = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.31662479, 1.68337521}
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