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Simplifying 5x2 + 2x2 = 80x + 32 Combine like terms: 5x2 + 2x2 = 7x2 7x2 = 80x + 32 Reorder the terms: 7x2 = 32 + 80x Solving 7x2 = 32 + 80x Solving for variable 'x'. Reorder the terms: -32 + -80x + 7x2 = 32 + 80x + -32 + -80x Reorder the terms: -32 + -80x + 7x2 = 32 + -32 + 80x + -80x Combine like terms: 32 + -32 = 0 -32 + -80x + 7x2 = 0 + 80x + -80x -32 + -80x + 7x2 = 80x + -80x Combine like terms: 80x + -80x = 0 -32 + -80x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -11.42857143x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -11.42857143x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -11.42857143x + x2 = 0 + 4.571428571 -11.42857143x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -11.42857143x + x2 = 4.571428571 The x term is -11.42857143x. Take half its coefficient (-5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. -11.42857143x + 32.65306123 + x2 = 4.571428571 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = 4.571428571 + 32.65306123 Combine like terms: 4.571428571 + 32.65306123 = 37.224489801 32.65306123 + -11.42857143x + x2 = 37.224489801 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 37.224489801 Calculate the square root of the right side: 6.101187573 Break this problem into two subproblems by setting (x + -5.714285715) equal to 6.101187573 and -6.101187573.Subproblem 1
x + -5.714285715 = 6.101187573 Simplifying x + -5.714285715 = 6.101187573 Reorder the terms: -5.714285715 + x = 6.101187573 Solving -5.714285715 + x = 6.101187573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = 6.101187573 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 6.101187573 + 5.714285715 x = 6.101187573 + 5.714285715 Combine like terms: 6.101187573 + 5.714285715 = 11.815473288 x = 11.815473288 Simplifying x = 11.815473288Subproblem 2
x + -5.714285715 = -6.101187573 Simplifying x + -5.714285715 = -6.101187573 Reorder the terms: -5.714285715 + x = -6.101187573 Solving -5.714285715 + x = -6.101187573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = -6.101187573 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -6.101187573 + 5.714285715 x = -6.101187573 + 5.714285715 Combine like terms: -6.101187573 + 5.714285715 = -0.386901858 x = -0.386901858 Simplifying x = -0.386901858Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.815473288, -0.386901858}
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