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Simplifying 160x + -60 + -7x2 = 0 Reorder the terms: -60 + 160x + -7x2 = 0 Solving -60 + 160x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 8.571428571 + -22.85714286x + x2 = 0 Move the constant term to the right: Add '-8.571428571' to each side of the equation. 8.571428571 + -22.85714286x + -8.571428571 + x2 = 0 + -8.571428571 Reorder the terms: 8.571428571 + -8.571428571 + -22.85714286x + x2 = 0 + -8.571428571 Combine like terms: 8.571428571 + -8.571428571 = 0.000000000 0.000000000 + -22.85714286x + x2 = 0 + -8.571428571 -22.85714286x + x2 = 0 + -8.571428571 Combine like terms: 0 + -8.571428571 = -8.571428571 -22.85714286x + x2 = -8.571428571 The x term is -22.85714286x. Take half its coefficient (-11.42857143). Square it (130.6122449) and add it to both sides. Add '130.6122449' to each side of the equation. -22.85714286x + 130.6122449 + x2 = -8.571428571 + 130.6122449 Reorder the terms: 130.6122449 + -22.85714286x + x2 = -8.571428571 + 130.6122449 Combine like terms: -8.571428571 + 130.6122449 = 122.040816329 130.6122449 + -22.85714286x + x2 = 122.040816329 Factor a perfect square on the left side: (x + -11.42857143)(x + -11.42857143) = 122.040816329 Calculate the square root of the right side: 11.047208531 Break this problem into two subproblems by setting (x + -11.42857143) equal to 11.047208531 and -11.047208531.Subproblem 1
x + -11.42857143 = 11.047208531 Simplifying x + -11.42857143 = 11.047208531 Reorder the terms: -11.42857143 + x = 11.047208531 Solving -11.42857143 + x = 11.047208531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.42857143' to each side of the equation. -11.42857143 + 11.42857143 + x = 11.047208531 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + x = 11.047208531 + 11.42857143 x = 11.047208531 + 11.42857143 Combine like terms: 11.047208531 + 11.42857143 = 22.475779961 x = 22.475779961 Simplifying x = 22.475779961Subproblem 2
x + -11.42857143 = -11.047208531 Simplifying x + -11.42857143 = -11.047208531 Reorder the terms: -11.42857143 + x = -11.047208531 Solving -11.42857143 + x = -11.047208531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.42857143' to each side of the equation. -11.42857143 + 11.42857143 + x = -11.047208531 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + x = -11.047208531 + 11.42857143 x = -11.047208531 + 11.42857143 Combine like terms: -11.047208531 + 11.42857143 = 0.381362899 x = 0.381362899 Simplifying x = 0.381362899Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.475779961, 0.381362899}
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