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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 = 64 64 + 81x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 64 + 81x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 81x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 81x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 81x + x2 = 0 + -64 81x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 81x + x2 = -64 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 = -64 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = -64 + 1640.25 Combine like terms: -64 + 1640.25 = 1576.25 1640.25 + 81x + x2 = 1576.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1576.25 Calculate the square root of the right side: 39.702015062 Break this problem into two subproblems by setting (x + 40.5) equal to 39.702015062 and -39.702015062.Subproblem 1
x + 40.5 = 39.702015062 Simplifying x + 40.5 = 39.702015062 Reorder the terms: 40.5 + x = 39.702015062 Solving 40.5 + x = 39.702015062 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 = 39.702015062 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 39.702015062 + -40.5 x = 39.702015062 + -40.5 Combine like terms: 39.702015062 + -40.5 = -0.797984938 x = -0.797984938 Simplifying x = -0.797984938Subproblem 2
x + 40.5 = -39.702015062 Simplifying x + 40.5 = -39.702015062 Reorder the terms: 40.5 + x = -39.702015062 Solving 40.5 + x = -39.702015062 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 = -39.702015062 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -39.702015062 + -40.5 x = -39.702015062 + -40.5 Combine like terms: -39.702015062 + -40.5 = -80.202015062 x = -80.202015062 Simplifying x = -80.202015062Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.797984938, -80.202015062}
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