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Simplifying x2 + -180x + -2700 = 0 Reorder the terms: -2700 + -180x + x2 = 0 Solving -2700 + -180x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + -180x + 2700 + x2 = 0 + 2700 Reorder the terms: -2700 + 2700 + -180x + x2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + -180x + x2 = 0 + 2700 -180x + x2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 -180x + x2 = 2700 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 = 2700 + 8100 Reorder the terms: 8100 + -180x + x2 = 2700 + 8100 Combine like terms: 2700 + 8100 = 10800 8100 + -180x + x2 = 10800 Factor a perfect square on the left side: (x + -90)(x + -90) = 10800 Calculate the square root of the right side: 103.923048454 Break this problem into two subproblems by setting (x + -90) equal to 103.923048454 and -103.923048454.Subproblem 1
x + -90 = 103.923048454 Simplifying x + -90 = 103.923048454 Reorder the terms: -90 + x = 103.923048454 Solving -90 + x = 103.923048454 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 = 103.923048454 + 90 Combine like terms: -90 + 90 = 0 0 + x = 103.923048454 + 90 x = 103.923048454 + 90 Combine like terms: 103.923048454 + 90 = 193.923048454 x = 193.923048454 Simplifying x = 193.923048454Subproblem 2
x + -90 = -103.923048454 Simplifying x + -90 = -103.923048454 Reorder the terms: -90 + x = -103.923048454 Solving -90 + x = -103.923048454 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 = -103.923048454 + 90 Combine like terms: -90 + 90 = 0 0 + x = -103.923048454 + 90 x = -103.923048454 + 90 Combine like terms: -103.923048454 + 90 = -13.923048454 x = -13.923048454 Simplifying x = -13.923048454Solution
The solution to the problem is based on the solutions from the subproblems. x = {193.923048454, -13.923048454}
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