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Simplifying x2 + -160x + 1120 = 0 Reorder the terms: 1120 + -160x + x2 = 0 Solving 1120 + -160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1120' to each side of the equation. 1120 + -160x + -1120 + x2 = 0 + -1120 Reorder the terms: 1120 + -1120 + -160x + x2 = 0 + -1120 Combine like terms: 1120 + -1120 = 0 0 + -160x + x2 = 0 + -1120 -160x + x2 = 0 + -1120 Combine like terms: 0 + -1120 = -1120 -160x + x2 = -1120 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -1120 + 6400 Reorder the terms: 6400 + -160x + x2 = -1120 + 6400 Combine like terms: -1120 + 6400 = 5280 6400 + -160x + x2 = 5280 Factor a perfect square on the left side: (x + -80)(x + -80) = 5280 Calculate the square root of the right side: 72.663608498 Break this problem into two subproblems by setting (x + -80) equal to 72.663608498 and -72.663608498.Subproblem 1
x + -80 = 72.663608498 Simplifying x + -80 = 72.663608498 Reorder the terms: -80 + x = 72.663608498 Solving -80 + x = 72.663608498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 72.663608498 + 80 Combine like terms: -80 + 80 = 0 0 + x = 72.663608498 + 80 x = 72.663608498 + 80 Combine like terms: 72.663608498 + 80 = 152.663608498 x = 152.663608498 Simplifying x = 152.663608498Subproblem 2
x + -80 = -72.663608498 Simplifying x + -80 = -72.663608498 Reorder the terms: -80 + x = -72.663608498 Solving -80 + x = -72.663608498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -72.663608498 + 80 Combine like terms: -80 + 80 = 0 0 + x = -72.663608498 + 80 x = -72.663608498 + 80 Combine like terms: -72.663608498 + 80 = 7.336391502 x = 7.336391502 Simplifying x = 7.336391502Solution
The solution to the problem is based on the solutions from the subproblems. x = {152.663608498, 7.336391502}
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