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Simplifying -2a2 + 8a + 11 = 0 Reorder the terms: 11 + 8a + -2a2 = 0 Solving 11 + 8a + -2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + -4a + a2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -4a + 5.5 + a2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -4a + a2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -4a + a2 = 0 + 5.5 -4a + a2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -4a + a2 = 5.5 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 = 5.5 + 4 Reorder the terms: 4 + -4a + a2 = 5.5 + 4 Combine like terms: 5.5 + 4 = 9.5 4 + -4a + a2 = 9.5 Factor a perfect square on the left side: (a + -2)(a + -2) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (a + -2) equal to 3.082207001 and -3.082207001.Subproblem 1
a + -2 = 3.082207001 Simplifying a + -2 = 3.082207001 Reorder the terms: -2 + a = 3.082207001 Solving -2 + a = 3.082207001 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 = 3.082207001 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.082207001 + 2 a = 3.082207001 + 2 Combine like terms: 3.082207001 + 2 = 5.082207001 a = 5.082207001 Simplifying a = 5.082207001Subproblem 2
a + -2 = -3.082207001 Simplifying a + -2 = -3.082207001 Reorder the terms: -2 + a = -3.082207001 Solving -2 + a = -3.082207001 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 = -3.082207001 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.082207001 + 2 a = -3.082207001 + 2 Combine like terms: -3.082207001 + 2 = -1.082207001 a = -1.082207001 Simplifying a = -1.082207001Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.082207001, -1.082207001}
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