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Simplifying 7x2 + 24x = -14 Reorder the terms: 24x + 7x2 = -14 Solving 24x + 7x2 = -14 Solving for variable 'x'. Reorder the terms: 14 + 24x + 7x2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + 24x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.428571429x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.428571429x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.428571429x + x2 = 0 + -2 3.428571429x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.428571429x + x2 = -2 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 = -2 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = -2 + 2.938775513 Combine like terms: -2 + 2.938775513 = 0.938775513 2.938775513 + 3.428571429x + x2 = 0.938775513 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 0.938775513 Calculate the square root of the right side: 0.968904285 Break this problem into two subproblems by setting (x + 1.714285715) equal to 0.968904285 and -0.968904285.Subproblem 1
x + 1.714285715 = 0.968904285 Simplifying x + 1.714285715 = 0.968904285 Reorder the terms: 1.714285715 + x = 0.968904285 Solving 1.714285715 + x = 0.968904285 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 = 0.968904285 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 0.968904285 + -1.714285715 x = 0.968904285 + -1.714285715 Combine like terms: 0.968904285 + -1.714285715 = -0.74538143 x = -0.74538143 Simplifying x = -0.74538143Subproblem 2
x + 1.714285715 = -0.968904285 Simplifying x + 1.714285715 = -0.968904285 Reorder the terms: 1.714285715 + x = -0.968904285 Solving 1.714285715 + x = -0.968904285 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 = -0.968904285 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -0.968904285 + -1.714285715 x = -0.968904285 + -1.714285715 Combine like terms: -0.968904285 + -1.714285715 = -2.68319 x = -2.68319 Simplifying x = -2.68319Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.74538143, -2.68319}
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