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Simplifying 7x2 = 8x + 11 Reorder the terms: 7x2 = 11 + 8x Solving 7x2 = 11 + 8x Solving for variable 'x'. Reorder the terms: -11 + -8x + 7x2 = 11 + 8x + -11 + -8x Reorder the terms: -11 + -8x + 7x2 = 11 + -11 + 8x + -8x Combine like terms: 11 + -11 = 0 -11 + -8x + 7x2 = 0 + 8x + -8x -11 + -8x + 7x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -11 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -1.142857143x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -1.142857143x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 1.571428571 -1.142857143x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -1.142857143x + x2 = 1.571428571 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 1.571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 1.571428571 + 0.3265306123 Combine like terms: 1.571428571 + 0.3265306123 = 1.8979591833 0.3265306123 + -1.142857143x + x2 = 1.8979591833 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.8979591833 Calculate the square root of the right side: 1.377664394 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.377664394 and -1.377664394.Subproblem 1
x + -0.5714285715 = 1.377664394 Simplifying x + -0.5714285715 = 1.377664394 Reorder the terms: -0.5714285715 + x = 1.377664394 Solving -0.5714285715 + x = 1.377664394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 1.377664394 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.377664394 + 0.5714285715 x = 1.377664394 + 0.5714285715 Combine like terms: 1.377664394 + 0.5714285715 = 1.9490929655 x = 1.9490929655 Simplifying x = 1.9490929655Subproblem 2
x + -0.5714285715 = -1.377664394 Simplifying x + -0.5714285715 = -1.377664394 Reorder the terms: -0.5714285715 + x = -1.377664394 Solving -0.5714285715 + x = -1.377664394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -1.377664394 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.377664394 + 0.5714285715 x = -1.377664394 + 0.5714285715 Combine like terms: -1.377664394 + 0.5714285715 = -0.8062358225 x = -0.8062358225 Simplifying x = -0.8062358225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9490929655, -0.8062358225}
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