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Simplifying x2 + -800x + 90000 = 0 Reorder the terms: 90000 + -800x + x2 = 0 Solving 90000 + -800x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90000' to each side of the equation. 90000 + -800x + -90000 + x2 = 0 + -90000 Reorder the terms: 90000 + -90000 + -800x + x2 = 0 + -90000 Combine like terms: 90000 + -90000 = 0 0 + -800x + x2 = 0 + -90000 -800x + x2 = 0 + -90000 Combine like terms: 0 + -90000 = -90000 -800x + x2 = -90000 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 = -90000 + 160000 Reorder the terms: 160000 + -800x + x2 = -90000 + 160000 Combine like terms: -90000 + 160000 = 70000 160000 + -800x + x2 = 70000 Factor a perfect square on the left side: (x + -400)(x + -400) = 70000 Calculate the square root of the right side: 264.575131106 Break this problem into two subproblems by setting (x + -400) equal to 264.575131106 and -264.575131106.Subproblem 1
x + -400 = 264.575131106 Simplifying x + -400 = 264.575131106 Reorder the terms: -400 + x = 264.575131106 Solving -400 + x = 264.575131106 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 = 264.575131106 + 400 Combine like terms: -400 + 400 = 0 0 + x = 264.575131106 + 400 x = 264.575131106 + 400 Combine like terms: 264.575131106 + 400 = 664.575131106 x = 664.575131106 Simplifying x = 664.575131106Subproblem 2
x + -400 = -264.575131106 Simplifying x + -400 = -264.575131106 Reorder the terms: -400 + x = -264.575131106 Solving -400 + x = -264.575131106 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 = -264.575131106 + 400 Combine like terms: -400 + 400 = 0 0 + x = -264.575131106 + 400 x = -264.575131106 + 400 Combine like terms: -264.575131106 + 400 = 135.424868894 x = 135.424868894 Simplifying x = 135.424868894Solution
The solution to the problem is based on the solutions from the subproblems. x = {664.575131106, 135.424868894}
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