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Simplifying x2 + -380x + 36050 = 0 Reorder the terms: 36050 + -380x + x2 = 0 Solving 36050 + -380x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36050' to each side of the equation. 36050 + -380x + -36050 + x2 = 0 + -36050 Reorder the terms: 36050 + -36050 + -380x + x2 = 0 + -36050 Combine like terms: 36050 + -36050 = 0 0 + -380x + x2 = 0 + -36050 -380x + x2 = 0 + -36050 Combine like terms: 0 + -36050 = -36050 -380x + x2 = -36050 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 = -36050 + 36100 Reorder the terms: 36100 + -380x + x2 = -36050 + 36100 Combine like terms: -36050 + 36100 = 50 36100 + -380x + x2 = 50 Factor a perfect square on the left side: (x + -190)(x + -190) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -190) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -190 = 7.071067812 Simplifying x + -190 = 7.071067812 Reorder the terms: -190 + x = 7.071067812 Solving -190 + x = 7.071067812 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 = 7.071067812 + 190 Combine like terms: -190 + 190 = 0 0 + x = 7.071067812 + 190 x = 7.071067812 + 190 Combine like terms: 7.071067812 + 190 = 197.071067812 x = 197.071067812 Simplifying x = 197.071067812Subproblem 2
x + -190 = -7.071067812 Simplifying x + -190 = -7.071067812 Reorder the terms: -190 + x = -7.071067812 Solving -190 + x = -7.071067812 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 = -7.071067812 + 190 Combine like terms: -190 + 190 = 0 0 + x = -7.071067812 + 190 x = -7.071067812 + 190 Combine like terms: -7.071067812 + 190 = 182.928932188 x = 182.928932188 Simplifying x = 182.928932188Solution
The solution to the problem is based on the solutions from the subproblems. x = {197.071067812, 182.928932188}
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