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Simplifying x2 + -180x + 1600 = 0 Reorder the terms: 1600 + -180x + x2 = 0 Solving 1600 + -180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + -180x + -1600 + x2 = 0 + -1600 Reorder the terms: 1600 + -1600 + -180x + x2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + -180x + x2 = 0 + -1600 -180x + x2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 -180x + x2 = -1600 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -1600 + 8100 Reorder the terms: 8100 + -180x + x2 = -1600 + 8100 Combine like terms: -1600 + 8100 = 6500 8100 + -180x + x2 = 6500 Factor a perfect square on the left side: (x + -90)(x + -90) = 6500 Calculate the square root of the right side: 80.622577483 Break this problem into two subproblems by setting (x + -90) equal to 80.622577483 and -80.622577483.Subproblem 1
x + -90 = 80.622577483 Simplifying x + -90 = 80.622577483 Reorder the terms: -90 + x = 80.622577483 Solving -90 + x = 80.622577483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 80.622577483 + 90 Combine like terms: -90 + 90 = 0 0 + x = 80.622577483 + 90 x = 80.622577483 + 90 Combine like terms: 80.622577483 + 90 = 170.622577483 x = 170.622577483 Simplifying x = 170.622577483Subproblem 2
x + -90 = -80.622577483 Simplifying x + -90 = -80.622577483 Reorder the terms: -90 + x = -80.622577483 Solving -90 + x = -80.622577483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -80.622577483 + 90 Combine like terms: -90 + 90 = 0 0 + x = -80.622577483 + 90 x = -80.622577483 + 90 Combine like terms: -80.622577483 + 90 = 9.377422517 x = 9.377422517 Simplifying x = 9.377422517Solution
The solution to the problem is based on the solutions from the subproblems. x = {170.622577483, 9.377422517}
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