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Simplifying a2 + -14a + 49 = 63 Reorder the terms: 49 + -14a + a2 = 63 Solving 49 + -14a + a2 = 63 Solving for variable 'a'. Reorder the terms: 49 + -63 + -14a + a2 = 63 + -63 Combine like terms: 49 + -63 = -14 -14 + -14a + a2 = 63 + -63 Combine like terms: 63 + -63 = 0 -14 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -14a + 14 + a2 = 0 + 14 Reorder the terms: -14 + 14 + -14a + a2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -14a + a2 = 0 + 14 -14a + a2 = 0 + 14 Combine like terms: 0 + 14 = 14 -14a + a2 = 14 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 = 14 + 49 Reorder the terms: 49 + -14a + a2 = 14 + 49 Combine like terms: 14 + 49 = 63 49 + -14a + a2 = 63 Factor a perfect square on the left side: (a + -7)(a + -7) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (a + -7) equal to 7.937253933 and -7.937253933.Subproblem 1
a + -7 = 7.937253933 Simplifying a + -7 = 7.937253933 Reorder the terms: -7 + a = 7.937253933 Solving -7 + a = 7.937253933 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 = 7.937253933 + 7 Combine like terms: -7 + 7 = 0 0 + a = 7.937253933 + 7 a = 7.937253933 + 7 Combine like terms: 7.937253933 + 7 = 14.937253933 a = 14.937253933 Simplifying a = 14.937253933Subproblem 2
a + -7 = -7.937253933 Simplifying a + -7 = -7.937253933 Reorder the terms: -7 + a = -7.937253933 Solving -7 + a = -7.937253933 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 = -7.937253933 + 7 Combine like terms: -7 + 7 = 0 0 + a = -7.937253933 + 7 a = -7.937253933 + 7 Combine like terms: -7.937253933 + 7 = -0.937253933 a = -0.937253933 Simplifying a = -0.937253933Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.937253933, -0.937253933}
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