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Simplifying 7x2 + -45x + -32 = 0 Reorder the terms: -32 + -45x + 7x2 = 0 Solving -32 + -45x + 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'. -4.571428571 + -6.428571429x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -6.428571429x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -6.428571429x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -6.428571429x + x2 = 0 + 4.571428571 -6.428571429x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -6.428571429x + x2 = 4.571428571 The x term is -6.428571429x. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429x + 10.33163266 + x2 = 4.571428571 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429x + x2 = 4.571428571 + 10.33163266 Combine like terms: 4.571428571 + 10.33163266 = 14.903061231 10.33163266 + -6.428571429x + x2 = 14.903061231 Factor a perfect square on the left side: (x + -3.214285715)(x + -3.214285715) = 14.903061231 Calculate the square root of the right side: 3.86044832 Break this problem into two subproblems by setting (x + -3.214285715) equal to 3.86044832 and -3.86044832.Subproblem 1
x + -3.214285715 = 3.86044832 Simplifying x + -3.214285715 = 3.86044832 Reorder the terms: -3.214285715 + x = 3.86044832 Solving -3.214285715 + x = 3.86044832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = 3.86044832 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = 3.86044832 + 3.214285715 x = 3.86044832 + 3.214285715 Combine like terms: 3.86044832 + 3.214285715 = 7.074734035 x = 7.074734035 Simplifying x = 7.074734035Subproblem 2
x + -3.214285715 = -3.86044832 Simplifying x + -3.214285715 = -3.86044832 Reorder the terms: -3.214285715 + x = -3.86044832 Solving -3.214285715 + x = -3.86044832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = -3.86044832 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = -3.86044832 + 3.214285715 x = -3.86044832 + 3.214285715 Combine like terms: -3.86044832 + 3.214285715 = -0.646162605 x = -0.646162605 Simplifying x = -0.646162605Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.074734035, -0.646162605}
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