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Simplifying 7x2 + -8x + -10 = 7 Reorder the terms: -10 + -8x + 7x2 = 7 Solving -10 + -8x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: -10 + -7 + -8x + 7x2 = 7 + -7 Combine like terms: -10 + -7 = -17 -17 + -8x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -17 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.428571429 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '2.428571429' to each side of the equation. -2.428571429 + -1.142857143x + 2.428571429 + x2 = 0 + 2.428571429 Reorder the terms: -2.428571429 + 2.428571429 + -1.142857143x + x2 = 0 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 2.428571429 -1.142857143x + x2 = 0 + 2.428571429 Combine like terms: 0 + 2.428571429 = 2.428571429 -1.142857143x + x2 = 2.428571429 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 = 2.428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 2.428571429 + 0.3265306123 Combine like terms: 2.428571429 + 0.3265306123 = 2.7551020413 0.3265306123 + -1.142857143x + x2 = 2.7551020413 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 2.7551020413 Calculate the square root of the right side: 1.659850006 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.659850006 and -1.659850006.Subproblem 1
x + -0.5714285715 = 1.659850006 Simplifying x + -0.5714285715 = 1.659850006 Reorder the terms: -0.5714285715 + x = 1.659850006 Solving -0.5714285715 + x = 1.659850006 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 = 1.659850006 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.659850006 + 0.5714285715 x = 1.659850006 + 0.5714285715 Combine like terms: 1.659850006 + 0.5714285715 = 2.2312785775 x = 2.2312785775 Simplifying x = 2.2312785775Subproblem 2
x + -0.5714285715 = -1.659850006 Simplifying x + -0.5714285715 = -1.659850006 Reorder the terms: -0.5714285715 + x = -1.659850006 Solving -0.5714285715 + x = -1.659850006 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 = -1.659850006 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.659850006 + 0.5714285715 x = -1.659850006 + 0.5714285715 Combine like terms: -1.659850006 + 0.5714285715 = -1.0884214345 x = -1.0884214345 Simplifying x = -1.0884214345Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2312785775, -1.0884214345}
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