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Simplifying 2x2 = 40x + 2 Reorder the terms: 2x2 = 2 + 40x Solving 2x2 = 2 + 40x Solving for variable 'x'. Reorder the terms: -2 + -40x + 2x2 = 2 + 40x + -2 + -40x Reorder the terms: -2 + -40x + 2x2 = 2 + -2 + 40x + -40x Combine like terms: 2 + -2 = 0 -2 + -40x + 2x2 = 0 + 40x + -40x -2 + -40x + 2x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -2 + -40x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -20x + x2)' equal to zero and attempt to solve: Simplifying -1 + -20x + x2 = 0 Solving -1 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -20x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -20x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -20x + x2 = 0 + 1 -20x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -20x + x2 = 1 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 1 + 100 Reorder the terms: 100 + -20x + x2 = 1 + 100 Combine like terms: 1 + 100 = 101 100 + -20x + x2 = 101 Factor a perfect square on the left side: (x + -10)(x + -10) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + -10) equal to 10.049875621 and -10.049875621.Subproblem 1
x + -10 = 10.049875621 Simplifying x + -10 = 10.049875621 Reorder the terms: -10 + x = 10.049875621 Solving -10 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.049875621 + 10 x = 10.049875621 + 10 Combine like terms: 10.049875621 + 10 = 20.049875621 x = 20.049875621 Simplifying x = 20.049875621Subproblem 2
x + -10 = -10.049875621 Simplifying x + -10 = -10.049875621 Reorder the terms: -10 + x = -10.049875621 Solving -10 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.049875621 + 10 x = -10.049875621 + 10 Combine like terms: -10.049875621 + 10 = -0.049875621 x = -0.049875621 Simplifying x = -0.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.049875621, -0.049875621}Solution
x = {20.049875621, -0.049875621}
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