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Simplifying 2a2 + 3a + -7 = 0 Reorder the terms: -7 + 3a + 2a2 = 0 Solving -7 + 3a + 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'. -3.5 + 1.5a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 1.5a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 1.5a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 1.5a + a2 = 0 + 3.5 1.5a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 1.5a + a2 = 3.5 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 = 3.5 + 0.5625 Reorder the terms: 0.5625 + 1.5a + a2 = 3.5 + 0.5625 Combine like terms: 3.5 + 0.5625 = 4.0625 0.5625 + 1.5a + a2 = 4.0625 Factor a perfect square on the left side: (a + 0.75)(a + 0.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (a + 0.75) equal to 2.015564437 and -2.015564437.Subproblem 1
a + 0.75 = 2.015564437 Simplifying a + 0.75 = 2.015564437 Reorder the terms: 0.75 + a = 2.015564437 Solving 0.75 + a = 2.015564437 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 = 2.015564437 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 2.015564437 + -0.75 a = 2.015564437 + -0.75 Combine like terms: 2.015564437 + -0.75 = 1.265564437 a = 1.265564437 Simplifying a = 1.265564437Subproblem 2
a + 0.75 = -2.015564437 Simplifying a + 0.75 = -2.015564437 Reorder the terms: 0.75 + a = -2.015564437 Solving 0.75 + a = -2.015564437 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 = -2.015564437 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -2.015564437 + -0.75 a = -2.015564437 + -0.75 Combine like terms: -2.015564437 + -0.75 = -2.765564437 a = -2.765564437 Simplifying a = -2.765564437Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.265564437, -2.765564437}
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