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Simplifying (x2) + -800x + -64 = 0 x2 + -800x + -64 = 0 Reorder the terms: -64 + -800x + x2 = 0 Solving -64 + -800x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -800x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -800x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -800x + x2 = 0 + 64 -800x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -800x + x2 = 64 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = 64 + 160000 Reorder the terms: 160000 + -800x + x2 = 64 + 160000 Combine like terms: 64 + 160000 = 160064 160000 + -800x + x2 = 160064 Factor a perfect square on the left side: (x + -400)(x + -400) = 160064 Calculate the square root of the right side: 400.079992002 Break this problem into two subproblems by setting (x + -400) equal to 400.079992002 and -400.079992002.Subproblem 1
x + -400 = 400.079992002 Simplifying x + -400 = 400.079992002 Reorder the terms: -400 + x = 400.079992002 Solving -400 + x = 400.079992002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 400.079992002 + 400 Combine like terms: -400 + 400 = 0 0 + x = 400.079992002 + 400 x = 400.079992002 + 400 Combine like terms: 400.079992002 + 400 = 800.079992002 x = 800.079992002 Simplifying x = 800.079992002Subproblem 2
x + -400 = -400.079992002 Simplifying x + -400 = -400.079992002 Reorder the terms: -400 + x = -400.079992002 Solving -400 + x = -400.079992002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -400.079992002 + 400 Combine like terms: -400 + 400 = 0 0 + x = -400.079992002 + 400 x = -400.079992002 + 400 Combine like terms: -400.079992002 + 400 = -0.079992002 x = -0.079992002 Simplifying x = -0.079992002Solution
The solution to the problem is based on the solutions from the subproblems. x = {800.079992002, -0.079992002}
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