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Simplifying a2 + -14a + 3 = -3 Reorder the terms: 3 + -14a + a2 = -3 Solving 3 + -14a + a2 = -3 Solving for variable 'a'. Reorder the terms: 3 + 3 + -14a + a2 = -3 + 3 Combine like terms: 3 + 3 = 6 6 + -14a + a2 = -3 + 3 Combine like terms: -3 + 3 = 0 6 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -14a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -14a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -14a + a2 = 0 + -6 -14a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -14a + a2 = -6 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 = -6 + 49 Reorder the terms: 49 + -14a + a2 = -6 + 49 Combine like terms: -6 + 49 = 43 49 + -14a + a2 = 43 Factor a perfect square on the left side: (a + -7)(a + -7) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (a + -7) equal to 6.557438524 and -6.557438524.Subproblem 1
a + -7 = 6.557438524 Simplifying a + -7 = 6.557438524 Reorder the terms: -7 + a = 6.557438524 Solving -7 + a = 6.557438524 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 = 6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + a = 6.557438524 + 7 a = 6.557438524 + 7 Combine like terms: 6.557438524 + 7 = 13.557438524 a = 13.557438524 Simplifying a = 13.557438524Subproblem 2
a + -7 = -6.557438524 Simplifying a + -7 = -6.557438524 Reorder the terms: -7 + a = -6.557438524 Solving -7 + a = -6.557438524 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 = -6.557438524 + 7 Combine like terms: -7 + 7 = 0 0 + a = -6.557438524 + 7 a = -6.557438524 + 7 Combine like terms: -6.557438524 + 7 = 0.442561476 a = 0.442561476 Simplifying a = 0.442561476Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.557438524, 0.442561476}
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