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Simplifying 7x2 + -28x + -60 = 0 Reorder the terms: -60 + -28x + 7x2 = 0 Solving -60 + -28x + 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 + -4x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + -4x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + -4x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + -4x + x2 = 0 + 8.571428571 -4x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 -4x + x2 = 8.571428571 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 8.571428571 + 4 Reorder the terms: 4 + -4x + x2 = 8.571428571 + 4 Combine like terms: 8.571428571 + 4 = 12.571428571 4 + -4x + x2 = 12.571428571 Factor a perfect square on the left side: (x + -2)(x + -2) = 12.571428571 Calculate the square root of the right side: 3.545621042 Break this problem into two subproblems by setting (x + -2) equal to 3.545621042 and -3.545621042.Subproblem 1
x + -2 = 3.545621042 Simplifying x + -2 = 3.545621042 Reorder the terms: -2 + x = 3.545621042 Solving -2 + x = 3.545621042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.545621042 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.545621042 + 2 x = 3.545621042 + 2 Combine like terms: 3.545621042 + 2 = 5.545621042 x = 5.545621042 Simplifying x = 5.545621042Subproblem 2
x + -2 = -3.545621042 Simplifying x + -2 = -3.545621042 Reorder the terms: -2 + x = -3.545621042 Solving -2 + x = -3.545621042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.545621042 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.545621042 + 2 x = -3.545621042 + 2 Combine like terms: -3.545621042 + 2 = -1.545621042 x = -1.545621042 Simplifying x = -1.545621042Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.545621042, -1.545621042}
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