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Simplifying 8a2 + 16a + -14 = 0 Reorder the terms: -14 + 16a + 8a2 = 0 Solving -14 + 16a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 8a + 4a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 8a + 4a2)' equal to zero and attempt to solve: Simplifying -7 + 8a + 4a2 = 0 Solving -7 + 8a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 2a + a2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 2a + 1.75 + a2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 2a + a2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 2a + a2 = 0 + 1.75 2a + a2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 2a + a2 = 1.75 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 = 1.75 + 1 Reorder the terms: 1 + 2a + a2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + 2a + a2 = 2.75 Factor a perfect square on the left side: (a + 1)(a + 1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (a + 1) equal to 1.658312395 and -1.658312395.Subproblem 1
a + 1 = 1.658312395 Simplifying a + 1 = 1.658312395 Reorder the terms: 1 + a = 1.658312395 Solving 1 + a = 1.658312395 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 = 1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.658312395 + -1 a = 1.658312395 + -1 Combine like terms: 1.658312395 + -1 = 0.658312395 a = 0.658312395 Simplifying a = 0.658312395Subproblem 2
a + 1 = -1.658312395 Simplifying a + 1 = -1.658312395 Reorder the terms: 1 + a = -1.658312395 Solving 1 + a = -1.658312395 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 = -1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.658312395 + -1 a = -1.658312395 + -1 Combine like terms: -1.658312395 + -1 = -2.658312395 a = -2.658312395 Simplifying a = -2.658312395Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.658312395, -2.658312395}Solution
a = {0.658312395, -2.658312395}
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