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Simplifying 7x2 + 9x + -60 = 0 Reorder the terms: -60 + 9x + 7x2 = 0 Solving -60 + 9x + 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 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + 1.285714286x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + 1.285714286x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + 1.285714286x + x2 = 0 + 8.571428571 1.285714286x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 1.285714286x + x2 = 8.571428571 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = 8.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = 8.571428571 + 0.4132653063 Combine like terms: 8.571428571 + 0.4132653063 = 8.9846938773 0.4132653063 + 1.285714286x + x2 = 8.9846938773 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 8.9846938773 Calculate the square root of the right side: 2.997447894 Break this problem into two subproblems by setting (x + 0.642857143) equal to 2.997447894 and -2.997447894.Subproblem 1
x + 0.642857143 = 2.997447894 Simplifying x + 0.642857143 = 2.997447894 Reorder the terms: 0.642857143 + x = 2.997447894 Solving 0.642857143 + x = 2.997447894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 2.997447894 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 2.997447894 + -0.642857143 x = 2.997447894 + -0.642857143 Combine like terms: 2.997447894 + -0.642857143 = 2.354590751 x = 2.354590751 Simplifying x = 2.354590751Subproblem 2
x + 0.642857143 = -2.997447894 Simplifying x + 0.642857143 = -2.997447894 Reorder the terms: 0.642857143 + x = -2.997447894 Solving 0.642857143 + x = -2.997447894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -2.997447894 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -2.997447894 + -0.642857143 x = -2.997447894 + -0.642857143 Combine like terms: -2.997447894 + -0.642857143 = -3.640305037 x = -3.640305037 Simplifying x = -3.640305037Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.354590751, -3.640305037}
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