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Simplifying 8x2 + -16x + -80 = 1 Reorder the terms: -80 + -16x + 8x2 = 1 Solving -80 + -16x + 8x2 = 1 Solving for variable 'x'. Reorder the terms: -80 + -1 + -16x + 8x2 = 1 + -1 Combine like terms: -80 + -1 = -81 -81 + -16x + 8x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -81 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10.125 + -2x + x2 = 0 Move the constant term to the right: Add '10.125' to each side of the equation. -10.125 + -2x + 10.125 + x2 = 0 + 10.125 Reorder the terms: -10.125 + 10.125 + -2x + x2 = 0 + 10.125 Combine like terms: -10.125 + 10.125 = 0.000 0.000 + -2x + x2 = 0 + 10.125 -2x + x2 = 0 + 10.125 Combine like terms: 0 + 10.125 = 10.125 -2x + x2 = 10.125 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 = 10.125 + 1 Reorder the terms: 1 + -2x + x2 = 10.125 + 1 Combine like terms: 10.125 + 1 = 11.125 1 + -2x + x2 = 11.125 Factor a perfect square on the left side: (x + -1)(x + -1) = 11.125 Calculate the square root of the right side: 3.335416016 Break this problem into two subproblems by setting (x + -1) equal to 3.335416016 and -3.335416016.Subproblem 1
x + -1 = 3.335416016 Simplifying x + -1 = 3.335416016 Reorder the terms: -1 + x = 3.335416016 Solving -1 + x = 3.335416016 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 = 3.335416016 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.335416016 + 1 x = 3.335416016 + 1 Combine like terms: 3.335416016 + 1 = 4.335416016 x = 4.335416016 Simplifying x = 4.335416016Subproblem 2
x + -1 = -3.335416016 Simplifying x + -1 = -3.335416016 Reorder the terms: -1 + x = -3.335416016 Solving -1 + x = -3.335416016 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 = -3.335416016 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.335416016 + 1 x = -3.335416016 + 1 Combine like terms: -3.335416016 + 1 = -2.335416016 x = -2.335416016 Simplifying x = -2.335416016Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.335416016, -2.335416016}
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