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Simplifying a2 + 4a + -54 = 0 Reorder the terms: -54 + 4a + a2 = 0 Solving -54 + 4a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 4a + 54 + a2 = 0 + 54 Reorder the terms: -54 + 54 + 4a + a2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 4a + a2 = 0 + 54 4a + a2 = 0 + 54 Combine like terms: 0 + 54 = 54 4a + a2 = 54 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 = 54 + 4 Reorder the terms: 4 + 4a + a2 = 54 + 4 Combine like terms: 54 + 4 = 58 4 + 4a + a2 = 58 Factor a perfect square on the left side: (a + 2)(a + 2) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (a + 2) equal to 7.615773106 and -7.615773106.Subproblem 1
a + 2 = 7.615773106 Simplifying a + 2 = 7.615773106 Reorder the terms: 2 + a = 7.615773106 Solving 2 + a = 7.615773106 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 = 7.615773106 + -2 Combine like terms: 2 + -2 = 0 0 + a = 7.615773106 + -2 a = 7.615773106 + -2 Combine like terms: 7.615773106 + -2 = 5.615773106 a = 5.615773106 Simplifying a = 5.615773106Subproblem 2
a + 2 = -7.615773106 Simplifying a + 2 = -7.615773106 Reorder the terms: 2 + a = -7.615773106 Solving 2 + a = -7.615773106 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 = -7.615773106 + -2 Combine like terms: 2 + -2 = 0 0 + a = -7.615773106 + -2 a = -7.615773106 + -2 Combine like terms: -7.615773106 + -2 = -9.615773106 a = -9.615773106 Simplifying a = -9.615773106Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.615773106, -9.615773106}
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