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Simplifying 11a2 + -15a + -25 = 0 Reorder the terms: -25 + -15a + 11a2 = 0 Solving -25 + -15a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.272727273 + -1.363636364a + a2 = 0 Move the constant term to the right: Add '2.272727273' to each side of the equation. -2.272727273 + -1.363636364a + 2.272727273 + a2 = 0 + 2.272727273 Reorder the terms: -2.272727273 + 2.272727273 + -1.363636364a + a2 = 0 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + -1.363636364a + a2 = 0 + 2.272727273 -1.363636364a + a2 = 0 + 2.272727273 Combine like terms: 0 + 2.272727273 = 2.272727273 -1.363636364a + a2 = 2.272727273 The a term is -1.363636364a. Take half its coefficient (-0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. -1.363636364a + 0.4648760333 + a2 = 2.272727273 + 0.4648760333 Reorder the terms: 0.4648760333 + -1.363636364a + a2 = 2.272727273 + 0.4648760333 Combine like terms: 2.272727273 + 0.4648760333 = 2.7376033063 0.4648760333 + -1.363636364a + a2 = 2.7376033063 Factor a perfect square on the left side: (a + -0.681818182)(a + -0.681818182) = 2.7376033063 Calculate the square root of the right side: 1.65457043 Break this problem into two subproblems by setting (a + -0.681818182) equal to 1.65457043 and -1.65457043.Subproblem 1
a + -0.681818182 = 1.65457043 Simplifying a + -0.681818182 = 1.65457043 Reorder the terms: -0.681818182 + a = 1.65457043 Solving -0.681818182 + a = 1.65457043 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + a = 1.65457043 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + a = 1.65457043 + 0.681818182 a = 1.65457043 + 0.681818182 Combine like terms: 1.65457043 + 0.681818182 = 2.336388612 a = 2.336388612 Simplifying a = 2.336388612Subproblem 2
a + -0.681818182 = -1.65457043 Simplifying a + -0.681818182 = -1.65457043 Reorder the terms: -0.681818182 + a = -1.65457043 Solving -0.681818182 + a = -1.65457043 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + a = -1.65457043 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + a = -1.65457043 + 0.681818182 a = -1.65457043 + 0.681818182 Combine like terms: -1.65457043 + 0.681818182 = -0.972752248 a = -0.972752248 Simplifying a = -0.972752248Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.336388612, -0.972752248}
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