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Simplifying 5x2 + -800x + 8000 = 0 Reorder the terms: 8000 + -800x + 5x2 = 0 Solving 8000 + -800x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1600 + -160x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1600 + -160x + x2)' equal to zero and attempt to solve: Simplifying 1600 + -160x + x2 = 0 Solving 1600 + -160x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -160x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -160x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -160x + x2 = 0 + -1600 -160x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -160x + x2 = -1600 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -1600 + 6400 Reorder the terms: 6400 + -160x + x2 = -1600 + 6400 Combine like terms: -1600 + 6400 = 4800 6400 + -160x + x2 = 4800 Factor a perfect square on the left side: (x + -80)(x + -80) = 4800 Calculate the square root of the right side: 69.282032303 Break this problem into two subproblems by setting (x + -80) equal to 69.282032303 and -69.282032303.Subproblem 1
x + -80 = 69.282032303 Simplifying x + -80 = 69.282032303 Reorder the terms: -80 + x = 69.282032303 Solving -80 + x = 69.282032303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 69.282032303 + 80 Combine like terms: -80 + 80 = 0 0 + x = 69.282032303 + 80 x = 69.282032303 + 80 Combine like terms: 69.282032303 + 80 = 149.282032303 x = 149.282032303 Simplifying x = 149.282032303Subproblem 2
x + -80 = -69.282032303 Simplifying x + -80 = -69.282032303 Reorder the terms: -80 + x = -69.282032303 Solving -80 + x = -69.282032303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -69.282032303 + 80 Combine like terms: -80 + 80 = 0 0 + x = -69.282032303 + 80 x = -69.282032303 + 80 Combine like terms: -69.282032303 + 80 = 10.717967697 x = 10.717967697 Simplifying x = 10.717967697Solution
The solution to the problem is based on the solutions from the subproblems. x = {149.282032303, 10.717967697}Solution
x = {149.282032303, 10.717967697}
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