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Simplifying 4a2 + -6a + -11 = 0 Reorder the terms: -11 + -6a + 4a2 = 0 Solving -11 + -6a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -1.5a + a2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -1.5a + 2.75 + a2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -1.5a + a2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -1.5a + a2 = 0 + 2.75 -1.5a + a2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -1.5a + a2 = 2.75 The a term is -1.5a. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5a + 0.5625 + a2 = 2.75 + 0.5625 Reorder the terms: 0.5625 + -1.5a + a2 = 2.75 + 0.5625 Combine like terms: 2.75 + 0.5625 = 3.3125 0.5625 + -1.5a + a2 = 3.3125 Factor a perfect square on the left side: (a + -0.75)(a + -0.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (a + -0.75) equal to 1.820027472 and -1.820027472.Subproblem 1
a + -0.75 = 1.820027472 Simplifying a + -0.75 = 1.820027472 Reorder the terms: -0.75 + a = 1.820027472 Solving -0.75 + a = 1.820027472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = 1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = 1.820027472 + 0.75 a = 1.820027472 + 0.75 Combine like terms: 1.820027472 + 0.75 = 2.570027472 a = 2.570027472 Simplifying a = 2.570027472Subproblem 2
a + -0.75 = -1.820027472 Simplifying a + -0.75 = -1.820027472 Reorder the terms: -0.75 + a = -1.820027472 Solving -0.75 + a = -1.820027472 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + a = -1.820027472 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + a = -1.820027472 + 0.75 a = -1.820027472 + 0.75 Combine like terms: -1.820027472 + 0.75 = -1.070027472 a = -1.070027472 Simplifying a = -1.070027472Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.570027472, -1.070027472}
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