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Simplifying 7x2 + 24x + -144 = 0 Reorder the terms: -144 + 24x + 7x2 = 0 Solving -144 + 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'. -20.57142857 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '20.57142857' to each side of the equation. -20.57142857 + 3.428571429x + 20.57142857 + x2 = 0 + 20.57142857 Reorder the terms: -20.57142857 + 20.57142857 + 3.428571429x + x2 = 0 + 20.57142857 Combine like terms: -20.57142857 + 20.57142857 = 0.00000000 0.00000000 + 3.428571429x + x2 = 0 + 20.57142857 3.428571429x + x2 = 0 + 20.57142857 Combine like terms: 0 + 20.57142857 = 20.57142857 3.428571429x + x2 = 20.57142857 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 = 20.57142857 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = 20.57142857 + 2.938775513 Combine like terms: 20.57142857 + 2.938775513 = 23.510204083 2.938775513 + 3.428571429x + x2 = 23.510204083 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 23.510204083 Calculate the square root of the right side: 4.848732214 Break this problem into two subproblems by setting (x + 1.714285715) equal to 4.848732214 and -4.848732214.Subproblem 1
x + 1.714285715 = 4.848732214 Simplifying x + 1.714285715 = 4.848732214 Reorder the terms: 1.714285715 + x = 4.848732214 Solving 1.714285715 + x = 4.848732214 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 = 4.848732214 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 4.848732214 + -1.714285715 x = 4.848732214 + -1.714285715 Combine like terms: 4.848732214 + -1.714285715 = 3.134446499 x = 3.134446499 Simplifying x = 3.134446499Subproblem 2
x + 1.714285715 = -4.848732214 Simplifying x + 1.714285715 = -4.848732214 Reorder the terms: 1.714285715 + x = -4.848732214 Solving 1.714285715 + x = -4.848732214 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 = -4.848732214 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -4.848732214 + -1.714285715 x = -4.848732214 + -1.714285715 Combine like terms: -4.848732214 + -1.714285715 = -6.563017929 x = -6.563017929 Simplifying x = -6.563017929Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.134446499, -6.563017929}
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