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Simplifying a2 + 6a + -300 = 0 Reorder the terms: -300 + 6a + a2 = 0 Solving -300 + 6a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 6a + 300 + a2 = 0 + 300 Reorder the terms: -300 + 300 + 6a + a2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 6a + a2 = 0 + 300 6a + a2 = 0 + 300 Combine like terms: 0 + 300 = 300 6a + a2 = 300 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 300 + 9 Reorder the terms: 9 + 6a + a2 = 300 + 9 Combine like terms: 300 + 9 = 309 9 + 6a + a2 = 309 Factor a perfect square on the left side: (a + 3)(a + 3) = 309 Calculate the square root of the right side: 17.578395831 Break this problem into two subproblems by setting (a + 3) equal to 17.578395831 and -17.578395831.Subproblem 1
a + 3 = 17.578395831 Simplifying a + 3 = 17.578395831 Reorder the terms: 3 + a = 17.578395831 Solving 3 + a = 17.578395831 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + a = 17.578395831 + -3 a = 17.578395831 + -3 Combine like terms: 17.578395831 + -3 = 14.578395831 a = 14.578395831 Simplifying a = 14.578395831Subproblem 2
a + 3 = -17.578395831 Simplifying a + 3 = -17.578395831 Reorder the terms: 3 + a = -17.578395831 Solving 3 + a = -17.578395831 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + a = -17.578395831 + -3 a = -17.578395831 + -3 Combine like terms: -17.578395831 + -3 = -20.578395831 a = -20.578395831 Simplifying a = -20.578395831Solution
The solution to the problem is based on the solutions from the subproblems. a = {14.578395831, -20.578395831}
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