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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 = 1.192325433 x = 1.192325433 Simplifying x = 1.192325433Subproblem 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 = -82.192325433 x = -82.192325433 Simplifying x = -82.192325433Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.192325433, -82.192325433}
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