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Simplifying 1.75x2 + -2x + -64 = 0 Reorder the terms: -64 + -2x + 1.75x2 = 0 Solving -64 + -2x + 1.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.75 the coefficient of the squared term: Divide each side by '1.75'. -36.57142857 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '36.57142857' to each side of the equation. -36.57142857 + -1.142857143x + 36.57142857 + x2 = 0 + 36.57142857 Reorder the terms: -36.57142857 + 36.57142857 + -1.142857143x + x2 = 0 + 36.57142857 Combine like terms: -36.57142857 + 36.57142857 = 0.00000000 0.00000000 + -1.142857143x + x2 = 0 + 36.57142857 -1.142857143x + x2 = 0 + 36.57142857 Combine like terms: 0 + 36.57142857 = 36.57142857 -1.142857143x + x2 = 36.57142857 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 36.57142857 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 36.57142857 + 0.3265306123 Combine like terms: 36.57142857 + 0.3265306123 = 36.8979591823 0.3265306123 + -1.142857143x + x2 = 36.8979591823 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 36.8979591823 Calculate the square root of the right side: 6.074369036 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 6.074369036 and -6.074369036.Subproblem 1
x + -0.5714285715 = 6.074369036 Simplifying x + -0.5714285715 = 6.074369036 Reorder the terms: -0.5714285715 + x = 6.074369036 Solving -0.5714285715 + x = 6.074369036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 6.074369036 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 6.074369036 + 0.5714285715 x = 6.074369036 + 0.5714285715 Combine like terms: 6.074369036 + 0.5714285715 = 6.6457976075 x = 6.6457976075 Simplifying x = 6.6457976075Subproblem 2
x + -0.5714285715 = -6.074369036 Simplifying x + -0.5714285715 = -6.074369036 Reorder the terms: -0.5714285715 + x = -6.074369036 Solving -0.5714285715 + x = -6.074369036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -6.074369036 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -6.074369036 + 0.5714285715 x = -6.074369036 + 0.5714285715 Combine like terms: -6.074369036 + 0.5714285715 = -5.5029404645 x = -5.5029404645 Simplifying x = -5.5029404645Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6457976075, -5.5029404645}
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