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Simplifying x2 + -380x + 5000 = 0 Reorder the terms: 5000 + -380x + x2 = 0 Solving 5000 + -380x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -380x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -380x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -380x + x2 = 0 + -5000 -380x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -380x + x2 = -5000 The x term is -380x. Take half its coefficient (-190). Square it (36100) and add it to both sides. Add '36100' to each side of the equation. -380x + 36100 + x2 = -5000 + 36100 Reorder the terms: 36100 + -380x + x2 = -5000 + 36100 Combine like terms: -5000 + 36100 = 31100 36100 + -380x + x2 = 31100 Factor a perfect square on the left side: (x + -190)(x + -190) = 31100 Calculate the square root of the right side: 176.351920885 Break this problem into two subproblems by setting (x + -190) equal to 176.351920885 and -176.351920885.Subproblem 1
x + -190 = 176.351920885 Simplifying x + -190 = 176.351920885 Reorder the terms: -190 + x = 176.351920885 Solving -190 + x = 176.351920885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '190' to each side of the equation. -190 + 190 + x = 176.351920885 + 190 Combine like terms: -190 + 190 = 0 0 + x = 176.351920885 + 190 x = 176.351920885 + 190 Combine like terms: 176.351920885 + 190 = 366.351920885 x = 366.351920885 Simplifying x = 366.351920885Subproblem 2
x + -190 = -176.351920885 Simplifying x + -190 = -176.351920885 Reorder the terms: -190 + x = -176.351920885 Solving -190 + x = -176.351920885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '190' to each side of the equation. -190 + 190 + x = -176.351920885 + 190 Combine like terms: -190 + 190 = 0 0 + x = -176.351920885 + 190 x = -176.351920885 + 190 Combine like terms: -176.351920885 + 190 = 13.648079115 x = 13.648079115 Simplifying x = 13.648079115Solution
The solution to the problem is based on the solutions from the subproblems. x = {366.351920885, 13.648079115}
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