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Simplifying 5x2 + -200x + -640000 = 0 Reorder the terms: -640000 + -200x + 5x2 = 0 Solving -640000 + -200x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-128000 + -40x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-128000 + -40x + x2)' equal to zero and attempt to solve: Simplifying -128000 + -40x + x2 = 0 Solving -128000 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128000' to each side of the equation. -128000 + -40x + 128000 + x2 = 0 + 128000 Reorder the terms: -128000 + 128000 + -40x + x2 = 0 + 128000 Combine like terms: -128000 + 128000 = 0 0 + -40x + x2 = 0 + 128000 -40x + x2 = 0 + 128000 Combine like terms: 0 + 128000 = 128000 -40x + x2 = 128000 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 = 128000 + 400 Reorder the terms: 400 + -40x + x2 = 128000 + 400 Combine like terms: 128000 + 400 = 128400 400 + -40x + x2 = 128400 Factor a perfect square on the left side: (x + -20)(x + -20) = 128400 Calculate the square root of the right side: 358.329457343 Break this problem into two subproblems by setting (x + -20) equal to 358.329457343 and -358.329457343.Subproblem 1
x + -20 = 358.329457343 Simplifying x + -20 = 358.329457343 Reorder the terms: -20 + x = 358.329457343 Solving -20 + x = 358.329457343 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 = 358.329457343 + 20 Combine like terms: -20 + 20 = 0 0 + x = 358.329457343 + 20 x = 358.329457343 + 20 Combine like terms: 358.329457343 + 20 = 378.329457343 x = 378.329457343 Simplifying x = 378.329457343Subproblem 2
x + -20 = -358.329457343 Simplifying x + -20 = -358.329457343 Reorder the terms: -20 + x = -358.329457343 Solving -20 + x = -358.329457343 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 = -358.329457343 + 20 Combine like terms: -20 + 20 = 0 0 + x = -358.329457343 + 20 x = -358.329457343 + 20 Combine like terms: -358.329457343 + 20 = -338.329457343 x = -338.329457343 Simplifying x = -338.329457343Solution
The solution to the problem is based on the solutions from the subproblems. x = {378.329457343, -338.329457343}Solution
x = {378.329457343, -338.329457343}
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