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Simplifying 2x2 + 80x + -2000 = 0 Reorder the terms: -2000 + 80x + 2x2 = 0 Solving -2000 + 80x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1000 + 40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1000 + 40x + x2)' equal to zero and attempt to solve: Simplifying -1000 + 40x + x2 = 0 Solving -1000 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 40x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 40x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 40x + x2 = 0 + 1000 40x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 40x + x2 = 1000 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 1000 + 400 Reorder the terms: 400 + 40x + x2 = 1000 + 400 Combine like terms: 1000 + 400 = 1400 400 + 40x + x2 = 1400 Factor a perfect square on the left side: (x + 20)(x + 20) = 1400 Calculate the square root of the right side: 37.416573868 Break this problem into two subproblems by setting (x + 20) equal to 37.416573868 and -37.416573868.Subproblem 1
x + 20 = 37.416573868 Simplifying x + 20 = 37.416573868 Reorder the terms: 20 + x = 37.416573868 Solving 20 + x = 37.416573868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 37.416573868 + -20 Combine like terms: 20 + -20 = 0 0 + x = 37.416573868 + -20 x = 37.416573868 + -20 Combine like terms: 37.416573868 + -20 = 17.416573868 x = 17.416573868 Simplifying x = 17.416573868Subproblem 2
x + 20 = -37.416573868 Simplifying x + 20 = -37.416573868 Reorder the terms: 20 + x = -37.416573868 Solving 20 + x = -37.416573868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -37.416573868 + -20 Combine like terms: 20 + -20 = 0 0 + x = -37.416573868 + -20 x = -37.416573868 + -20 Combine like terms: -37.416573868 + -20 = -57.416573868 x = -57.416573868 Simplifying x = -57.416573868Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.416573868, -57.416573868}Solution
x = {17.416573868, -57.416573868}
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