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Simplifying 8x2 + -16x + -97 = 0 Reorder the terms: -97 + -16x + 8x2 = 0 Solving -97 + -16x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.125 + -2x + x2 = 0 Move the constant term to the right: Add '12.125' to each side of the equation. -12.125 + -2x + 12.125 + x2 = 0 + 12.125 Reorder the terms: -12.125 + 12.125 + -2x + x2 = 0 + 12.125 Combine like terms: -12.125 + 12.125 = 0.000 0.000 + -2x + x2 = 0 + 12.125 -2x + x2 = 0 + 12.125 Combine like terms: 0 + 12.125 = 12.125 -2x + x2 = 12.125 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 = 12.125 + 1 Reorder the terms: 1 + -2x + x2 = 12.125 + 1 Combine like terms: 12.125 + 1 = 13.125 1 + -2x + x2 = 13.125 Factor a perfect square on the left side: (x + -1)(x + -1) = 13.125 Calculate the square root of the right side: 3.622844187 Break this problem into two subproblems by setting (x + -1) equal to 3.622844187 and -3.622844187.Subproblem 1
x + -1 = 3.622844187 Simplifying x + -1 = 3.622844187 Reorder the terms: -1 + x = 3.622844187 Solving -1 + x = 3.622844187 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 = 3.622844187 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.622844187 + 1 x = 3.622844187 + 1 Combine like terms: 3.622844187 + 1 = 4.622844187 x = 4.622844187 Simplifying x = 4.622844187Subproblem 2
x + -1 = -3.622844187 Simplifying x + -1 = -3.622844187 Reorder the terms: -1 + x = -3.622844187 Solving -1 + x = -3.622844187 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 = -3.622844187 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.622844187 + 1 x = -3.622844187 + 1 Combine like terms: -3.622844187 + 1 = -2.622844187 x = -2.622844187 Simplifying x = -2.622844187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.622844187, -2.622844187}
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