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Simplifying 7x2 + -42x + -60 = 0 Reorder the terms: -60 + -42x + 7x2 = 0 Solving -60 + -42x + 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 + -6x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + -6x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + -6x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + -6x + x2 = 0 + 8.571428571 -6x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 -6x + x2 = 8.571428571 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 8.571428571 + 9 Reorder the terms: 9 + -6x + x2 = 8.571428571 + 9 Combine like terms: 8.571428571 + 9 = 17.571428571 9 + -6x + x2 = 17.571428571 Factor a perfect square on the left side: (x + -3)(x + -3) = 17.571428571 Calculate the square root of the right side: 4.191828786 Break this problem into two subproblems by setting (x + -3) equal to 4.191828786 and -4.191828786.Subproblem 1
x + -3 = 4.191828786 Simplifying x + -3 = 4.191828786 Reorder the terms: -3 + x = 4.191828786 Solving -3 + x = 4.191828786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.191828786 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.191828786 + 3 x = 4.191828786 + 3 Combine like terms: 4.191828786 + 3 = 7.191828786 x = 7.191828786 Simplifying x = 7.191828786Subproblem 2
x + -3 = -4.191828786 Simplifying x + -3 = -4.191828786 Reorder the terms: -3 + x = -4.191828786 Solving -3 + x = -4.191828786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.191828786 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.191828786 + 3 x = -4.191828786 + 3 Combine like terms: -4.191828786 + 3 = -1.191828786 x = -1.191828786 Simplifying x = -1.191828786Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.191828786, -1.191828786}
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