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Simplifying x2 + -900x + 100000 = 0 Reorder the terms: 100000 + -900x + x2 = 0 Solving 100000 + -900x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100000' to each side of the equation. 100000 + -900x + -100000 + x2 = 0 + -100000 Reorder the terms: 100000 + -100000 + -900x + x2 = 0 + -100000 Combine like terms: 100000 + -100000 = 0 0 + -900x + x2 = 0 + -100000 -900x + x2 = 0 + -100000 Combine like terms: 0 + -100000 = -100000 -900x + x2 = -100000 The x term is -900x. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900x + 202500 + x2 = -100000 + 202500 Reorder the terms: 202500 + -900x + x2 = -100000 + 202500 Combine like terms: -100000 + 202500 = 102500 202500 + -900x + x2 = 102500 Factor a perfect square on the left side: (x + -450)(x + -450) = 102500 Calculate the square root of the right side: 320.156211872 Break this problem into two subproblems by setting (x + -450) equal to 320.156211872 and -320.156211872.Subproblem 1
x + -450 = 320.156211872 Simplifying x + -450 = 320.156211872 Reorder the terms: -450 + x = 320.156211872 Solving -450 + x = 320.156211872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 320.156211872 + 450 Combine like terms: -450 + 450 = 0 0 + x = 320.156211872 + 450 x = 320.156211872 + 450 Combine like terms: 320.156211872 + 450 = 770.156211872 x = 770.156211872 Simplifying x = 770.156211872Subproblem 2
x + -450 = -320.156211872 Simplifying x + -450 = -320.156211872 Reorder the terms: -450 + x = -320.156211872 Solving -450 + x = -320.156211872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = -320.156211872 + 450 Combine like terms: -450 + 450 = 0 0 + x = -320.156211872 + 450 x = -320.156211872 + 450 Combine like terms: -320.156211872 + 450 = 129.843788128 x = 129.843788128 Simplifying x = 129.843788128Solution
The solution to the problem is based on the solutions from the subproblems. x = {770.156211872, 129.843788128}
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