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Simplifying x2 + -800x + -12000 = 0 Reorder the terms: -12000 + -800x + x2 = 0 Solving -12000 + -800x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12000' to each side of the equation. -12000 + -800x + 12000 + x2 = 0 + 12000 Reorder the terms: -12000 + 12000 + -800x + x2 = 0 + 12000 Combine like terms: -12000 + 12000 = 0 0 + -800x + x2 = 0 + 12000 -800x + x2 = 0 + 12000 Combine like terms: 0 + 12000 = 12000 -800x + x2 = 12000 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 = 12000 + 160000 Reorder the terms: 160000 + -800x + x2 = 12000 + 160000 Combine like terms: 12000 + 160000 = 172000 160000 + -800x + x2 = 172000 Factor a perfect square on the left side: (x + -400)(x + -400) = 172000 Calculate the square root of the right side: 414.728827067 Break this problem into two subproblems by setting (x + -400) equal to 414.728827067 and -414.728827067.Subproblem 1
x + -400 = 414.728827067 Simplifying x + -400 = 414.728827067 Reorder the terms: -400 + x = 414.728827067 Solving -400 + x = 414.728827067 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 = 414.728827067 + 400 Combine like terms: -400 + 400 = 0 0 + x = 414.728827067 + 400 x = 414.728827067 + 400 Combine like terms: 414.728827067 + 400 = 814.728827067 x = 814.728827067 Simplifying x = 814.728827067Subproblem 2
x + -400 = -414.728827067 Simplifying x + -400 = -414.728827067 Reorder the terms: -400 + x = -414.728827067 Solving -400 + x = -414.728827067 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 = -414.728827067 + 400 Combine like terms: -400 + 400 = 0 0 + x = -414.728827067 + 400 x = -414.728827067 + 400 Combine like terms: -414.728827067 + 400 = -14.728827067 x = -14.728827067 Simplifying x = -14.728827067Solution
The solution to the problem is based on the solutions from the subproblems. x = {814.728827067, -14.728827067}
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