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Simplifying 8.75x2 + -1x = 1 Reorder the terms: -1x + 8.75x2 = 1 Solving -1x + 8.75x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -1x + 8.75x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -1x + 8.75x2 = 0 Begin completing the square. Divide all terms by 8.75 the coefficient of the squared term: Divide each side by '8.75'. -0.1142857143 + -0.1142857143x + x2 = 0 Move the constant term to the right: Add '0.1142857143' to each side of the equation. -0.1142857143 + -0.1142857143x + 0.1142857143 + x2 = 0 + 0.1142857143 Reorder the terms: -0.1142857143 + 0.1142857143 + -0.1142857143x + x2 = 0 + 0.1142857143 Combine like terms: -0.1142857143 + 0.1142857143 = 0.0000000000 0.0000000000 + -0.1142857143x + x2 = 0 + 0.1142857143 -0.1142857143x + x2 = 0 + 0.1142857143 Combine like terms: 0 + 0.1142857143 = 0.1142857143 -0.1142857143x + x2 = 0.1142857143 The x term is -0.1142857143x. Take half its coefficient (-0.05714285715). Square it (0.003265306123) and add it to both sides. Add '0.003265306123' to each side of the equation. -0.1142857143x + 0.003265306123 + x2 = 0.1142857143 + 0.003265306123 Reorder the terms: 0.003265306123 + -0.1142857143x + x2 = 0.1142857143 + 0.003265306123 Combine like terms: 0.1142857143 + 0.003265306123 = 0.117551020423 0.003265306123 + -0.1142857143x + x2 = 0.117551020423 Factor a perfect square on the left side: (x + -0.05714285715)(x + -0.05714285715) = 0.117551020423 Calculate the square root of the right side: 0.342857143 Break this problem into two subproblems by setting (x + -0.05714285715) equal to 0.342857143 and -0.342857143.Subproblem 1
x + -0.05714285715 = 0.342857143 Simplifying x + -0.05714285715 = 0.342857143 Reorder the terms: -0.05714285715 + x = 0.342857143 Solving -0.05714285715 + x = 0.342857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05714285715' to each side of the equation. -0.05714285715 + 0.05714285715 + x = 0.342857143 + 0.05714285715 Combine like terms: -0.05714285715 + 0.05714285715 = 0.00000000000 0.00000000000 + x = 0.342857143 + 0.05714285715 x = 0.342857143 + 0.05714285715 Combine like terms: 0.342857143 + 0.05714285715 = 0.40000000015 x = 0.40000000015 Simplifying x = 0.40000000015Subproblem 2
x + -0.05714285715 = -0.342857143 Simplifying x + -0.05714285715 = -0.342857143 Reorder the terms: -0.05714285715 + x = -0.342857143 Solving -0.05714285715 + x = -0.342857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05714285715' to each side of the equation. -0.05714285715 + 0.05714285715 + x = -0.342857143 + 0.05714285715 Combine like terms: -0.05714285715 + 0.05714285715 = 0.00000000000 0.00000000000 + x = -0.342857143 + 0.05714285715 x = -0.342857143 + 0.05714285715 Combine like terms: -0.342857143 + 0.05714285715 = -0.28571428585 x = -0.28571428585 Simplifying x = -0.28571428585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.40000000015, -0.28571428585}
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