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Simplifying 7x2 + 24x + -35 = 0 Reorder the terms: -35 + 24x + 7x2 = 0 Solving -35 + 24x + 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'. -5 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.428571429x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3.428571429x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.428571429x + x2 = 0 + 5 3.428571429x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.428571429x + x2 = 5 The x term is 3.428571429x. Take half its coefficient (1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. 3.428571429x + 2.938775513 + x2 = 5 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = 5 + 2.938775513 Combine like terms: 5 + 2.938775513 = 7.938775513 2.938775513 + 3.428571429x + x2 = 7.938775513 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 7.938775513 Calculate the square root of the right side: 2.817583275 Break this problem into two subproblems by setting (x + 1.714285715) equal to 2.817583275 and -2.817583275.Subproblem 1
x + 1.714285715 = 2.817583275 Simplifying x + 1.714285715 = 2.817583275 Reorder the terms: 1.714285715 + x = 2.817583275 Solving 1.714285715 + x = 2.817583275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = 2.817583275 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 2.817583275 + -1.714285715 x = 2.817583275 + -1.714285715 Combine like terms: 2.817583275 + -1.714285715 = 1.10329756 x = 1.10329756 Simplifying x = 1.10329756Subproblem 2
x + 1.714285715 = -2.817583275 Simplifying x + 1.714285715 = -2.817583275 Reorder the terms: 1.714285715 + x = -2.817583275 Solving 1.714285715 + x = -2.817583275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = -2.817583275 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -2.817583275 + -1.714285715 x = -2.817583275 + -1.714285715 Combine like terms: -2.817583275 + -1.714285715 = -4.53186899 x = -4.53186899 Simplifying x = -4.53186899Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.10329756, -4.53186899}
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