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Simplifying 8x2 = 16x + -7.1 Reorder the terms: 8x2 = -7.1 + 16x Solving 8x2 = -7.1 + 16x Solving for variable 'x'. Reorder the terms: 7.1 + -16x + 8x2 = -7.1 + 16x + 7.1 + -16x Reorder the terms: 7.1 + -16x + 8x2 = -7.1 + 7.1 + 16x + -16x Combine like terms: -7.1 + 7.1 = 0.0 7.1 + -16x + 8x2 = 0.0 + 16x + -16x 7.1 + -16x + 8x2 = 16x + -16x Combine like terms: 16x + -16x = 0 7.1 + -16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.8875 + -2x + x2 = 0 Move the constant term to the right: Add '-0.8875' to each side of the equation. 0.8875 + -2x + -0.8875 + x2 = 0 + -0.8875 Reorder the terms: 0.8875 + -0.8875 + -2x + x2 = 0 + -0.8875 Combine like terms: 0.8875 + -0.8875 = 0.0000 0.0000 + -2x + x2 = 0 + -0.8875 -2x + x2 = 0 + -0.8875 Combine like terms: 0 + -0.8875 = -0.8875 -2x + x2 = -0.8875 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 = -0.8875 + 1 Reorder the terms: 1 + -2x + x2 = -0.8875 + 1 Combine like terms: -0.8875 + 1 = 0.1125 1 + -2x + x2 = 0.1125 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.1125 Calculate the square root of the right side: 0.335410197 Break this problem into two subproblems by setting (x + -1) equal to 0.335410197 and -0.335410197.Subproblem 1
x + -1 = 0.335410197 Simplifying x + -1 = 0.335410197 Reorder the terms: -1 + x = 0.335410197 Solving -1 + x = 0.335410197 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 = 0.335410197 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.335410197 + 1 x = 0.335410197 + 1 Combine like terms: 0.335410197 + 1 = 1.335410197 x = 1.335410197 Simplifying x = 1.335410197Subproblem 2
x + -1 = -0.335410197 Simplifying x + -1 = -0.335410197 Reorder the terms: -1 + x = -0.335410197 Solving -1 + x = -0.335410197 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 = -0.335410197 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.335410197 + 1 x = -0.335410197 + 1 Combine like terms: -0.335410197 + 1 = 0.664589803 x = 0.664589803 Simplifying x = 0.664589803Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.335410197, 0.664589803}
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