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Simplifying 7x2 + -66x + 9 = 0 Reorder the terms: 9 + -66x + 7x2 = 0 Solving 9 + -66x + 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'. 1.285714286 + -9.428571429x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -9.428571429x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -9.428571429x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -9.428571429x + x2 = 0 + -1.285714286 -9.428571429x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -9.428571429x + x2 = -1.285714286 The x term is -9.428571429x. Take half its coefficient (-4.714285715). Square it (22.22448980) and add it to both sides. Add '22.22448980' to each side of the equation. -9.428571429x + 22.22448980 + x2 = -1.285714286 + 22.22448980 Reorder the terms: 22.22448980 + -9.428571429x + x2 = -1.285714286 + 22.22448980 Combine like terms: -1.285714286 + 22.22448980 = 20.938775514 22.22448980 + -9.428571429x + x2 = 20.938775514 Factor a perfect square on the left side: (x + -4.714285715)(x + -4.714285715) = 20.938775514 Calculate the square root of the right side: 4.57589068 Break this problem into two subproblems by setting (x + -4.714285715) equal to 4.57589068 and -4.57589068.Subproblem 1
x + -4.714285715 = 4.57589068 Simplifying x + -4.714285715 = 4.57589068 Reorder the terms: -4.714285715 + x = 4.57589068 Solving -4.714285715 + x = 4.57589068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = 4.57589068 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = 4.57589068 + 4.714285715 x = 4.57589068 + 4.714285715 Combine like terms: 4.57589068 + 4.714285715 = 9.290176395 x = 9.290176395 Simplifying x = 9.290176395Subproblem 2
x + -4.714285715 = -4.57589068 Simplifying x + -4.714285715 = -4.57589068 Reorder the terms: -4.714285715 + x = -4.57589068 Solving -4.714285715 + x = -4.57589068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = -4.57589068 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = -4.57589068 + 4.714285715 x = -4.57589068 + 4.714285715 Combine like terms: -4.57589068 + 4.714285715 = 0.138395035 x = 0.138395035 Simplifying x = 0.138395035Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.290176395, 0.138395035}
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