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Simplifying a2 + -14a + 4 = 0 Reorder the terms: 4 + -14a + a2 = 0 Solving 4 + -14a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -14a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -14a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -14a + a2 = 0 + -4 -14a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -14a + a2 = -4 The a term is -14a. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14a + 49 + a2 = -4 + 49 Reorder the terms: 49 + -14a + a2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + -14a + a2 = 45 Factor a perfect square on the left side: (a + -7)(a + -7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (a + -7) equal to 6.708203933 and -6.708203933.Subproblem 1
a + -7 = 6.708203933 Simplifying a + -7 = 6.708203933 Reorder the terms: -7 + a = 6.708203933 Solving -7 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + a = 6.708203933 + 7 a = 6.708203933 + 7 Combine like terms: 6.708203933 + 7 = 13.708203933 a = 13.708203933 Simplifying a = 13.708203933Subproblem 2
a + -7 = -6.708203933 Simplifying a + -7 = -6.708203933 Reorder the terms: -7 + a = -6.708203933 Solving -7 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -6.708203933 + 7 Combine like terms: -7 + 7 = 0 0 + a = -6.708203933 + 7 a = -6.708203933 + 7 Combine like terms: -6.708203933 + 7 = 0.291796067 a = 0.291796067 Simplifying a = 0.291796067Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.708203933, 0.291796067}
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