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Simplifying 7x2 + 36x + -60 = 0 Reorder the terms: -60 + 36x + 7x2 = 0 Solving -60 + 36x + 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 + 5.142857143x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + 5.142857143x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + 5.142857143x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + 5.142857143x + x2 = 0 + 8.571428571 5.142857143x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 5.142857143x + x2 = 8.571428571 The x term is 5.142857143x. Take half its coefficient (2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. 5.142857143x + 6.612244901 + x2 = 8.571428571 + 6.612244901 Reorder the terms: 6.612244901 + 5.142857143x + x2 = 8.571428571 + 6.612244901 Combine like terms: 8.571428571 + 6.612244901 = 15.183673472 6.612244901 + 5.142857143x + x2 = 15.183673472 Factor a perfect square on the left side: (x + 2.571428572)(x + 2.571428572) = 15.183673472 Calculate the square root of the right side: 3.896623342 Break this problem into two subproblems by setting (x + 2.571428572) equal to 3.896623342 and -3.896623342.Subproblem 1
x + 2.571428572 = 3.896623342 Simplifying x + 2.571428572 = 3.896623342 Reorder the terms: 2.571428572 + x = 3.896623342 Solving 2.571428572 + x = 3.896623342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = 3.896623342 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = 3.896623342 + -2.571428572 x = 3.896623342 + -2.571428572 Combine like terms: 3.896623342 + -2.571428572 = 1.32519477 x = 1.32519477 Simplifying x = 1.32519477Subproblem 2
x + 2.571428572 = -3.896623342 Simplifying x + 2.571428572 = -3.896623342 Reorder the terms: 2.571428572 + x = -3.896623342 Solving 2.571428572 + x = -3.896623342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = -3.896623342 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = -3.896623342 + -2.571428572 x = -3.896623342 + -2.571428572 Combine like terms: -3.896623342 + -2.571428572 = -6.468051914 x = -6.468051914 Simplifying x = -6.468051914Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.32519477, -6.468051914}
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