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Simplifying x2 + -81x + -81 = 17 Reorder the terms: -81 + -81x + x2 = 17 Solving -81 + -81x + x2 = 17 Solving for variable 'x'. Reorder the terms: -81 + -17 + -81x + x2 = 17 + -17 Combine like terms: -81 + -17 = -98 -98 + -81x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -98 + -81x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -81x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -81x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -81x + x2 = 0 + 98 -81x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -81x + x2 = 98 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 = 98 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = 98 + 1640.25 Combine like terms: 98 + 1640.25 = 1738.25 1640.25 + -81x + x2 = 1738.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1738.25 Calculate the square root of the right side: 41.692325433 Break this problem into two subproblems by setting (x + -40.5) equal to 41.692325433 and -41.692325433.Subproblem 1
x + -40.5 = 41.692325433 Simplifying x + -40.5 = 41.692325433 Reorder the terms: -40.5 + x = 41.692325433 Solving -40.5 + x = 41.692325433 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 = 41.692325433 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 41.692325433 + 40.5 x = 41.692325433 + 40.5 Combine like terms: 41.692325433 + 40.5 = 82.192325433 x = 82.192325433 Simplifying x = 82.192325433Subproblem 2
x + -40.5 = -41.692325433 Simplifying x + -40.5 = -41.692325433 Reorder the terms: -40.5 + x = -41.692325433 Solving -40.5 + x = -41.692325433 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 = -41.692325433 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -41.692325433 + 40.5 x = -41.692325433 + 40.5 Combine like terms: -41.692325433 + 40.5 = -1.192325433 x = -1.192325433 Simplifying x = -1.192325433Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.192325433, -1.192325433}
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