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Simplifying 11(x + 14)(x + 14) = 250 Reorder the terms: 11(14 + x)(x + 14) = 250 Reorder the terms: 11(14 + x)(14 + x) = 250 Multiply (14 + x) * (14 + x) 11(14(14 + x) + x(14 + x)) = 250 11((14 * 14 + x * 14) + x(14 + x)) = 250 11((196 + 14x) + x(14 + x)) = 250 11(196 + 14x + (14 * x + x * x)) = 250 11(196 + 14x + (14x + x2)) = 250 Combine like terms: 14x + 14x = 28x 11(196 + 28x + x2) = 250 (196 * 11 + 28x * 11 + x2 * 11) = 250 (2156 + 308x + 11x2) = 250 Solving 2156 + 308x + 11x2 = 250 Solving for variable 'x'. Reorder the terms: 2156 + -250 + 308x + 11x2 = 250 + -250 Combine like terms: 2156 + -250 = 1906 1906 + 308x + 11x2 = 250 + -250 Combine like terms: 250 + -250 = 0 1906 + 308x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 173.2727273 + 28x + x2 = 0 Move the constant term to the right: Add '-173.2727273' to each side of the equation. 173.2727273 + 28x + -173.2727273 + x2 = 0 + -173.2727273 Reorder the terms: 173.2727273 + -173.2727273 + 28x + x2 = 0 + -173.2727273 Combine like terms: 173.2727273 + -173.2727273 = 0.0000000 0.0000000 + 28x + x2 = 0 + -173.2727273 28x + x2 = 0 + -173.2727273 Combine like terms: 0 + -173.2727273 = -173.2727273 28x + x2 = -173.2727273 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -173.2727273 + 196 Reorder the terms: 196 + 28x + x2 = -173.2727273 + 196 Combine like terms: -173.2727273 + 196 = 22.7272727 196 + 28x + x2 = 22.7272727 Factor a perfect square on the left side: (x + 14)(x + 14) = 22.7272727 Calculate the square root of the right side: 4.767312943 Break this problem into two subproblems by setting (x + 14) equal to 4.767312943 and -4.767312943.Subproblem 1
x + 14 = 4.767312943 Simplifying x + 14 = 4.767312943 Reorder the terms: 14 + x = 4.767312943 Solving 14 + x = 4.767312943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 4.767312943 + -14 Combine like terms: 14 + -14 = 0 0 + x = 4.767312943 + -14 x = 4.767312943 + -14 Combine like terms: 4.767312943 + -14 = -9.232687057 x = -9.232687057 Simplifying x = -9.232687057Subproblem 2
x + 14 = -4.767312943 Simplifying x + 14 = -4.767312943 Reorder the terms: 14 + x = -4.767312943 Solving 14 + x = -4.767312943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -4.767312943 + -14 Combine like terms: 14 + -14 = 0 0 + x = -4.767312943 + -14 x = -4.767312943 + -14 Combine like terms: -4.767312943 + -14 = -18.767312943 x = -18.767312943 Simplifying x = -18.767312943Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.232687057, -18.767312943}
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