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Simplifying 7x2 + -45x + -20 = 0 Reorder the terms: -20 + -45x + 7x2 = 0 Solving -20 + -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'. -2.857142857 + -6.428571429x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -6.428571429x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -6.428571429x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -6.428571429x + x2 = 0 + 2.857142857 -6.428571429x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -6.428571429x + x2 = 2.857142857 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 = 2.857142857 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429x + x2 = 2.857142857 + 10.33163266 Combine like terms: 2.857142857 + 10.33163266 = 13.188775517 10.33163266 + -6.428571429x + x2 = 13.188775517 Factor a perfect square on the left side: (x + -3.214285715)(x + -3.214285715) = 13.188775517 Calculate the square root of the right side: 3.631635378 Break this problem into two subproblems by setting (x + -3.214285715) equal to 3.631635378 and -3.631635378.Subproblem 1
x + -3.214285715 = 3.631635378 Simplifying x + -3.214285715 = 3.631635378 Reorder the terms: -3.214285715 + x = 3.631635378 Solving -3.214285715 + x = 3.631635378 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 = 3.631635378 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = 3.631635378 + 3.214285715 x = 3.631635378 + 3.214285715 Combine like terms: 3.631635378 + 3.214285715 = 6.845921093 x = 6.845921093 Simplifying x = 6.845921093Subproblem 2
x + -3.214285715 = -3.631635378 Simplifying x + -3.214285715 = -3.631635378 Reorder the terms: -3.214285715 + x = -3.631635378 Solving -3.214285715 + x = -3.631635378 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 = -3.631635378 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = -3.631635378 + 3.214285715 x = -3.631635378 + 3.214285715 Combine like terms: -3.631635378 + 3.214285715 = -0.417349663 x = -0.417349663 Simplifying x = -0.417349663Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.845921093, -0.417349663}
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