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Simplifying a2 + 4a + -91 = 7 Reorder the terms: -91 + 4a + a2 = 7 Solving -91 + 4a + a2 = 7 Solving for variable 'a'. Reorder the terms: -91 + -7 + 4a + a2 = 7 + -7 Combine like terms: -91 + -7 = -98 -98 + 4a + a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -98 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 4a + 98 + a2 = 0 + 98 Reorder the terms: -98 + 98 + 4a + a2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 4a + a2 = 0 + 98 4a + a2 = 0 + 98 Combine like terms: 0 + 98 = 98 4a + a2 = 98 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 98 + 4 Reorder the terms: 4 + 4a + a2 = 98 + 4 Combine like terms: 98 + 4 = 102 4 + 4a + a2 = 102 Factor a perfect square on the left side: (a + 2)(a + 2) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (a + 2) equal to 10.099504938 and -10.099504938.Subproblem 1
a + 2 = 10.099504938 Simplifying a + 2 = 10.099504938 Reorder the terms: 2 + a = 10.099504938 Solving 2 + a = 10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 10.099504938 + -2 Combine like terms: 2 + -2 = 0 0 + a = 10.099504938 + -2 a = 10.099504938 + -2 Combine like terms: 10.099504938 + -2 = 8.099504938 a = 8.099504938 Simplifying a = 8.099504938Subproblem 2
a + 2 = -10.099504938 Simplifying a + 2 = -10.099504938 Reorder the terms: 2 + a = -10.099504938 Solving 2 + a = -10.099504938 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -10.099504938 + -2 Combine like terms: 2 + -2 = 0 0 + a = -10.099504938 + -2 a = -10.099504938 + -2 Combine like terms: -10.099504938 + -2 = -12.099504938 a = -12.099504938 Simplifying a = -12.099504938Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.099504938, -12.099504938}
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