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Simplifying 160a2 + -6400a + -1600 = 0 Reorder the terms: -1600 + -6400a + 160a2 = 0 Solving -1600 + -6400a + 160a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '160'. 160(-10 + -40a + a2) = 0 Ignore the factor 160.Subproblem 1
Set the factor '(-10 + -40a + a2)' equal to zero and attempt to solve: Simplifying -10 + -40a + a2 = 0 Solving -10 + -40a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -40a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + -40a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -40a + a2 = 0 + 10 -40a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 -40a + a2 = 10 The a term is -40a. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40a + 400 + a2 = 10 + 400 Reorder the terms: 400 + -40a + a2 = 10 + 400 Combine like terms: 10 + 400 = 410 400 + -40a + a2 = 410 Factor a perfect square on the left side: (a + -20)(a + -20) = 410 Calculate the square root of the right side: 20.248456731 Break this problem into two subproblems by setting (a + -20) equal to 20.248456731 and -20.248456731.Subproblem 1
a + -20 = 20.248456731 Simplifying a + -20 = 20.248456731 Reorder the terms: -20 + a = 20.248456731 Solving -20 + a = 20.248456731 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = 20.248456731 + 20 Combine like terms: -20 + 20 = 0 0 + a = 20.248456731 + 20 a = 20.248456731 + 20 Combine like terms: 20.248456731 + 20 = 40.248456731 a = 40.248456731 Simplifying a = 40.248456731Subproblem 2
a + -20 = -20.248456731 Simplifying a + -20 = -20.248456731 Reorder the terms: -20 + a = -20.248456731 Solving -20 + a = -20.248456731 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + a = -20.248456731 + 20 Combine like terms: -20 + 20 = 0 0 + a = -20.248456731 + 20 a = -20.248456731 + 20 Combine like terms: -20.248456731 + 20 = -0.248456731 a = -0.248456731 Simplifying a = -0.248456731Solution
The solution to the problem is based on the solutions from the subproblems. a = {40.248456731, -0.248456731}Solution
a = {40.248456731, -0.248456731}
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