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Simplifying 2a2 + -152a = 180 Reorder the terms: -152a + 2a2 = 180 Solving -152a + 2a2 = 180 Solving for variable 'a'. Reorder the terms: -180 + -152a + 2a2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -152a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -76a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -76a + a2)' equal to zero and attempt to solve: Simplifying -90 + -76a + a2 = 0 Solving -90 + -76a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -76a + 90 + a2 = 0 + 90 Reorder the terms: -90 + 90 + -76a + a2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -76a + a2 = 0 + 90 -76a + a2 = 0 + 90 Combine like terms: 0 + 90 = 90 -76a + a2 = 90 The a term is -76a. Take half its coefficient (-38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. -76a + 1444 + a2 = 90 + 1444 Reorder the terms: 1444 + -76a + a2 = 90 + 1444 Combine like terms: 90 + 1444 = 1534 1444 + -76a + a2 = 1534 Factor a perfect square on the left side: (a + -38)(a + -38) = 1534 Calculate the square root of the right side: 39.166312055 Break this problem into two subproblems by setting (a + -38) equal to 39.166312055 and -39.166312055.Subproblem 1
a + -38 = 39.166312055 Simplifying a + -38 = 39.166312055 Reorder the terms: -38 + a = 39.166312055 Solving -38 + a = 39.166312055 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + a = 39.166312055 + 38 Combine like terms: -38 + 38 = 0 0 + a = 39.166312055 + 38 a = 39.166312055 + 38 Combine like terms: 39.166312055 + 38 = 77.166312055 a = 77.166312055 Simplifying a = 77.166312055Subproblem 2
a + -38 = -39.166312055 Simplifying a + -38 = -39.166312055 Reorder the terms: -38 + a = -39.166312055 Solving -38 + a = -39.166312055 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + a = -39.166312055 + 38 Combine like terms: -38 + 38 = 0 0 + a = -39.166312055 + 38 a = -39.166312055 + 38 Combine like terms: -39.166312055 + 38 = -1.166312055 a = -1.166312055 Simplifying a = -1.166312055Solution
The solution to the problem is based on the solutions from the subproblems. a = {77.166312055, -1.166312055}Solution
a = {77.166312055, -1.166312055}
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