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Simplifying x2 + -81x + 600 = 0 Reorder the terms: 600 + -81x + x2 = 0 Solving 600 + -81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + -81x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -81x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -81x + x2 = 0 + -600 -81x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -81x + x2 = -600 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 = -600 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = -600 + 1640.25 Combine like terms: -600 + 1640.25 = 1040.25 1640.25 + -81x + x2 = 1040.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1040.25 Calculate the square root of the right side: 32.252906846 Break this problem into two subproblems by setting (x + -40.5) equal to 32.252906846 and -32.252906846.Subproblem 1
x + -40.5 = 32.252906846 Simplifying x + -40.5 = 32.252906846 Reorder the terms: -40.5 + x = 32.252906846 Solving -40.5 + x = 32.252906846 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 = 32.252906846 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 32.252906846 + 40.5 x = 32.252906846 + 40.5 Combine like terms: 32.252906846 + 40.5 = 72.752906846 x = 72.752906846 Simplifying x = 72.752906846Subproblem 2
x + -40.5 = -32.252906846 Simplifying x + -40.5 = -32.252906846 Reorder the terms: -40.5 + x = -32.252906846 Solving -40.5 + x = -32.252906846 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 = -32.252906846 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -32.252906846 + 40.5 x = -32.252906846 + 40.5 Combine like terms: -32.252906846 + 40.5 = 8.247093154 x = 8.247093154 Simplifying x = 8.247093154Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.752906846, 8.247093154}
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