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Simplifying x2 + -81x + 180 = 0 Reorder the terms: 180 + -81x + x2 = 0 Solving 180 + -81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -81x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -81x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -81x + x2 = 0 + -180 -81x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -81x + x2 = -180 The x term is -81x. Take half its coefficient (-40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. -81x + 1640.25 + x2 = -180 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = -180 + 1640.25 Combine like terms: -180 + 1640.25 = 1460.25 1640.25 + -81x + x2 = 1460.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1460.25 Calculate the square root of the right side: 38.213217609 Break this problem into two subproblems by setting (x + -40.5) equal to 38.213217609 and -38.213217609.Subproblem 1
x + -40.5 = 38.213217609 Simplifying x + -40.5 = 38.213217609 Reorder the terms: -40.5 + x = 38.213217609 Solving -40.5 + x = 38.213217609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 38.213217609 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 38.213217609 + 40.5 x = 38.213217609 + 40.5 Combine like terms: 38.213217609 + 40.5 = 78.713217609 x = 78.713217609 Simplifying x = 78.713217609Subproblem 2
x + -40.5 = -38.213217609 Simplifying x + -40.5 = -38.213217609 Reorder the terms: -40.5 + x = -38.213217609 Solving -40.5 + x = -38.213217609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -38.213217609 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -38.213217609 + 40.5 x = -38.213217609 + 40.5 Combine like terms: -38.213217609 + 40.5 = 2.286782391 x = 2.286782391 Simplifying x = 2.286782391Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.713217609, 2.286782391}
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