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Simplifying 4x2 + 160x + -8000 = 0 Reorder the terms: -8000 + 160x + 4x2 = 0 Solving -8000 + 160x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2000 + 40x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2000 + 40x + x2)' equal to zero and attempt to solve: Simplifying -2000 + 40x + x2 = 0 Solving -2000 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 40x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 40x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 40x + x2 = 0 + 2000 40x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 40x + x2 = 2000 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 = 2000 + 400 Reorder the terms: 400 + 40x + x2 = 2000 + 400 Combine like terms: 2000 + 400 = 2400 400 + 40x + x2 = 2400 Factor a perfect square on the left side: (x + 20)(x + 20) = 2400 Calculate the square root of the right side: 48.989794856 Break this problem into two subproblems by setting (x + 20) equal to 48.989794856 and -48.989794856.Subproblem 1
x + 20 = 48.989794856 Simplifying x + 20 = 48.989794856 Reorder the terms: 20 + x = 48.989794856 Solving 20 + x = 48.989794856 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 = 48.989794856 + -20 Combine like terms: 20 + -20 = 0 0 + x = 48.989794856 + -20 x = 48.989794856 + -20 Combine like terms: 48.989794856 + -20 = 28.989794856 x = 28.989794856 Simplifying x = 28.989794856Subproblem 2
x + 20 = -48.989794856 Simplifying x + 20 = -48.989794856 Reorder the terms: 20 + x = -48.989794856 Solving 20 + x = -48.989794856 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 = -48.989794856 + -20 Combine like terms: 20 + -20 = 0 0 + x = -48.989794856 + -20 x = -48.989794856 + -20 Combine like terms: -48.989794856 + -20 = -68.989794856 x = -68.989794856 Simplifying x = -68.989794856Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.989794856, -68.989794856}Solution
x = {28.989794856, -68.989794856}
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