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Simplifying 4a2 + 16a + -1 = 2 Reorder the terms: -1 + 16a + 4a2 = 2 Solving -1 + 16a + 4a2 = 2 Solving for variable 'a'. Reorder the terms: -1 + -2 + 16a + 4a2 = 2 + -2 Combine like terms: -1 + -2 = -3 -3 + 16a + 4a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -3 + 16a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 4a + a2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 4a + 0.75 + a2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 4a + a2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 4a + a2 = 0 + 0.75 4a + a2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 4a + a2 = 0.75 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 = 0.75 + 4 Reorder the terms: 4 + 4a + a2 = 0.75 + 4 Combine like terms: 0.75 + 4 = 4.75 4 + 4a + a2 = 4.75 Factor a perfect square on the left side: (a + 2)(a + 2) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (a + 2) equal to 2.179449472 and -2.179449472.Subproblem 1
a + 2 = 2.179449472 Simplifying a + 2 = 2.179449472 Reorder the terms: 2 + a = 2.179449472 Solving 2 + a = 2.179449472 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 = 2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.179449472 + -2 a = 2.179449472 + -2 Combine like terms: 2.179449472 + -2 = 0.179449472 a = 0.179449472 Simplifying a = 0.179449472Subproblem 2
a + 2 = -2.179449472 Simplifying a + 2 = -2.179449472 Reorder the terms: 2 + a = -2.179449472 Solving 2 + a = -2.179449472 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 = -2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.179449472 + -2 a = -2.179449472 + -2 Combine like terms: -2.179449472 + -2 = -4.179449472 a = -4.179449472 Simplifying a = -4.179449472Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.179449472, -4.179449472}
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