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Simplifying x2 + -81x = 17 Reorder the terms: -81x + x2 = 17 Solving -81x + x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -81x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -81x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -81x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -81x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -81x + x2 = 0 + 17 -81x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -81x + x2 = 17 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 = 17 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = 17 + 1640.25 Combine like terms: 17 + 1640.25 = 1657.25 1640.25 + -81x + x2 = 1657.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1657.25 Calculate the square root of the right side: 40.709335539 Break this problem into two subproblems by setting (x + -40.5) equal to 40.709335539 and -40.709335539.Subproblem 1
x + -40.5 = 40.709335539 Simplifying x + -40.5 = 40.709335539 Reorder the terms: -40.5 + x = 40.709335539 Solving -40.5 + x = 40.709335539 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 = 40.709335539 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 40.709335539 + 40.5 x = 40.709335539 + 40.5 Combine like terms: 40.709335539 + 40.5 = 81.209335539 x = 81.209335539 Simplifying x = 81.209335539Subproblem 2
x + -40.5 = -40.709335539 Simplifying x + -40.5 = -40.709335539 Reorder the terms: -40.5 + x = -40.709335539 Solving -40.5 + x = -40.709335539 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 = -40.709335539 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -40.709335539 + 40.5 x = -40.709335539 + 40.5 Combine like terms: -40.709335539 + 40.5 = -0.209335539 x = -0.209335539 Simplifying x = -0.209335539Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.209335539, -0.209335539}
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