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Simplifying 8a2 + -16a + 3 = 4 Reorder the terms: 3 + -16a + 8a2 = 4 Solving 3 + -16a + 8a2 = 4 Solving for variable 'a'. Reorder the terms: 3 + -4 + -16a + 8a2 = 4 + -4 Combine like terms: 3 + -4 = -1 -1 + -16a + 8a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1 + -16a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -2a + a2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -2a + 0.125 + a2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -2a + a2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -2a + a2 = 0 + 0.125 -2a + a2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -2a + a2 = 0.125 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 = 0.125 + 1 Reorder the terms: 1 + -2a + a2 = 0.125 + 1 Combine like terms: 0.125 + 1 = 1.125 1 + -2a + a2 = 1.125 Factor a perfect square on the left side: (a + -1)(a + -1) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (a + -1) equal to 1.060660172 and -1.060660172.Subproblem 1
a + -1 = 1.060660172 Simplifying a + -1 = 1.060660172 Reorder the terms: -1 + a = 1.060660172 Solving -1 + a = 1.060660172 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 = 1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.060660172 + 1 a = 1.060660172 + 1 Combine like terms: 1.060660172 + 1 = 2.060660172 a = 2.060660172 Simplifying a = 2.060660172Subproblem 2
a + -1 = -1.060660172 Simplifying a + -1 = -1.060660172 Reorder the terms: -1 + a = -1.060660172 Solving -1 + a = -1.060660172 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 = -1.060660172 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.060660172 + 1 a = -1.060660172 + 1 Combine like terms: -1.060660172 + 1 = -0.060660172 a = -0.060660172 Simplifying a = -0.060660172Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.060660172, -0.060660172}
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