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Simplifying 2a2 + 4a + -3 = 0 Reorder the terms: -3 + 4a + 2a2 = 0 Solving -3 + 4a + 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'. -1.5 + 2a + a2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2a + 1.5 + a2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2a + a2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2a + a2 = 0 + 1.5 2a + a2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2a + a2 = 1.5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 1.5 + 1 Reorder the terms: 1 + 2a + a2 = 1.5 + 1 Combine like terms: 1.5 + 1 = 2.5 1 + 2a + a2 = 2.5 Factor a perfect square on the left side: (a + 1)(a + 1) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (a + 1) equal to 1.58113883 and -1.58113883.Subproblem 1
a + 1 = 1.58113883 Simplifying a + 1 = 1.58113883 Reorder the terms: 1 + a = 1.58113883 Solving 1 + a = 1.58113883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 1.58113883 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.58113883 + -1 a = 1.58113883 + -1 Combine like terms: 1.58113883 + -1 = 0.58113883 a = 0.58113883 Simplifying a = 0.58113883Subproblem 2
a + 1 = -1.58113883 Simplifying a + 1 = -1.58113883 Reorder the terms: 1 + a = -1.58113883 Solving 1 + a = -1.58113883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -1.58113883 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.58113883 + -1 a = -1.58113883 + -1 Combine like terms: -1.58113883 + -1 = -2.58113883 a = -2.58113883 Simplifying a = -2.58113883Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.58113883, -2.58113883}
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