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Simplifying x2 = 81x + -100 Reorder the terms: x2 = -100 + 81x Solving x2 = -100 + 81x Solving for variable 'x'. Reorder the terms: 100 + -81x + x2 = -100 + 81x + 100 + -81x Reorder the terms: 100 + -81x + x2 = -100 + 100 + 81x + -81x Combine like terms: -100 + 100 = 0 100 + -81x + x2 = 0 + 81x + -81x 100 + -81x + x2 = 81x + -81x Combine like terms: 81x + -81x = 0 100 + -81x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -81x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -81x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -81x + x2 = 0 + -100 -81x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -81x + x2 = -100 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 = -100 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = -100 + 1640.25 Combine like terms: -100 + 1640.25 = 1540.25 1640.25 + -81x + x2 = 1540.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1540.25 Calculate the square root of the right side: 39.246018906 Break this problem into two subproblems by setting (x + -40.5) equal to 39.246018906 and -39.246018906.Subproblem 1
x + -40.5 = 39.246018906 Simplifying x + -40.5 = 39.246018906 Reorder the terms: -40.5 + x = 39.246018906 Solving -40.5 + x = 39.246018906 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 = 39.246018906 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 39.246018906 + 40.5 x = 39.246018906 + 40.5 Combine like terms: 39.246018906 + 40.5 = 79.746018906 x = 79.746018906 Simplifying x = 79.746018906Subproblem 2
x + -40.5 = -39.246018906 Simplifying x + -40.5 = -39.246018906 Reorder the terms: -40.5 + x = -39.246018906 Solving -40.5 + x = -39.246018906 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 = -39.246018906 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -39.246018906 + 40.5 x = -39.246018906 + 40.5 Combine like terms: -39.246018906 + 40.5 = 1.253981094 x = 1.253981094 Simplifying x = 1.253981094Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.746018906, 1.253981094}
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