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Simplifying 81x2 + -162x + -81 = 4 Reorder the terms: -81 + -162x + 81x2 = 4 Solving -81 + -162x + 81x2 = 4 Solving for variable 'x'. Reorder the terms: -81 + -4 + -162x + 81x2 = 4 + -4 Combine like terms: -81 + -4 = -85 -85 + -162x + 81x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -85 + -162x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -1.049382716 + -2x + x2 = 0 Move the constant term to the right: Add '1.049382716' to each side of the equation. -1.049382716 + -2x + 1.049382716 + x2 = 0 + 1.049382716 Reorder the terms: -1.049382716 + 1.049382716 + -2x + x2 = 0 + 1.049382716 Combine like terms: -1.049382716 + 1.049382716 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.049382716 -2x + x2 = 0 + 1.049382716 Combine like terms: 0 + 1.049382716 = 1.049382716 -2x + x2 = 1.049382716 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.049382716 + 1 Reorder the terms: 1 + -2x + x2 = 1.049382716 + 1 Combine like terms: 1.049382716 + 1 = 2.049382716 1 + -2x + x2 = 2.049382716 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.049382716 Calculate the square root of the right side: 1.431566525 Break this problem into two subproblems by setting (x + -1) equal to 1.431566525 and -1.431566525.Subproblem 1
x + -1 = 1.431566525 Simplifying x + -1 = 1.431566525 Reorder the terms: -1 + x = 1.431566525 Solving -1 + x = 1.431566525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.431566525 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.431566525 + 1 x = 1.431566525 + 1 Combine like terms: 1.431566525 + 1 = 2.431566525 x = 2.431566525 Simplifying x = 2.431566525Subproblem 2
x + -1 = -1.431566525 Simplifying x + -1 = -1.431566525 Reorder the terms: -1 + x = -1.431566525 Solving -1 + x = -1.431566525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.431566525 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.431566525 + 1 x = -1.431566525 + 1 Combine like terms: -1.431566525 + 1 = -0.431566525 x = -0.431566525 Simplifying x = -0.431566525Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.431566525, -0.431566525}
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