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Simplifying x2 + 81x + 8 + -24 = 0 Reorder the terms: 8 + -24 + 81x + x2 = 0 Combine like terms: 8 + -24 = -16 -16 + 81x + x2 = 0 Solving -16 + 81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 81x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 81x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 81x + x2 = 0 + 16 81x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 81x + x2 = 16 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 = 16 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 16 + 1640.25 Combine like terms: 16 + 1640.25 = 1656.25 1640.25 + 81x + x2 = 1656.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1656.25 Calculate the square root of the right side: 40.69705149 Break this problem into two subproblems by setting (x + 40.5) equal to 40.69705149 and -40.69705149.Subproblem 1
x + 40.5 = 40.69705149 Simplifying x + 40.5 = 40.69705149 Reorder the terms: 40.5 + x = 40.69705149 Solving 40.5 + x = 40.69705149 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 = 40.69705149 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 40.69705149 + -40.5 x = 40.69705149 + -40.5 Combine like terms: 40.69705149 + -40.5 = 0.19705149 x = 0.19705149 Simplifying x = 0.19705149Subproblem 2
x + 40.5 = -40.69705149 Simplifying x + 40.5 = -40.69705149 Reorder the terms: 40.5 + x = -40.69705149 Solving 40.5 + x = -40.69705149 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 = -40.69705149 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -40.69705149 + -40.5 x = -40.69705149 + -40.5 Combine like terms: -40.69705149 + -40.5 = -81.19705149 x = -81.19705149 Simplifying x = -81.19705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19705149, -81.19705149}
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