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Simplifying 2x2 + -40x + 400 = 36x Reorder the terms: 400 + -40x + 2x2 = 36x Solving 400 + -40x + 2x2 = 36x Solving for variable 'x'. Reorder the terms: 400 + -40x + -36x + 2x2 = 36x + -36x Combine like terms: -40x + -36x = -76x 400 + -76x + 2x2 = 36x + -36x Combine like terms: 36x + -36x = 0 400 + -76x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -38x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + -38x + x2)' equal to zero and attempt to solve: Simplifying 200 + -38x + x2 = 0 Solving 200 + -38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -38x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -38x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -38x + x2 = 0 + -200 -38x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -38x + x2 = -200 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = -200 + 361 Reorder the terms: 361 + -38x + x2 = -200 + 361 Combine like terms: -200 + 361 = 161 361 + -38x + x2 = 161 Factor a perfect square on the left side: (x + -19)(x + -19) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + -19) equal to 12.68857754 and -12.68857754.Subproblem 1
x + -19 = 12.68857754 Simplifying x + -19 = 12.68857754 Reorder the terms: -19 + x = 12.68857754 Solving -19 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 12.68857754 + 19 Combine like terms: -19 + 19 = 0 0 + x = 12.68857754 + 19 x = 12.68857754 + 19 Combine like terms: 12.68857754 + 19 = 31.68857754 x = 31.68857754 Simplifying x = 31.68857754Subproblem 2
x + -19 = -12.68857754 Simplifying x + -19 = -12.68857754 Reorder the terms: -19 + x = -12.68857754 Solving -19 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -12.68857754 + 19 Combine like terms: -19 + 19 = 0 0 + x = -12.68857754 + 19 x = -12.68857754 + 19 Combine like terms: -12.68857754 + 19 = 6.31142246 x = 6.31142246 Simplifying x = 6.31142246Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.68857754, 6.31142246}Solution
x = {31.68857754, 6.31142246}
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