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Simplifying 2x(x + 49) = 435 Reorder the terms: 2x(49 + x) = 435 (49 * 2x + x * 2x) = 435 (98x + 2x2) = 435 Solving 98x + 2x2 = 435 Solving for variable 'x'. Reorder the terms: -435 + 98x + 2x2 = 435 + -435 Combine like terms: 435 + -435 = 0 -435 + 98x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -217.5 + 49x + x2 = 0 Move the constant term to the right: Add '217.5' to each side of the equation. -217.5 + 49x + 217.5 + x2 = 0 + 217.5 Reorder the terms: -217.5 + 217.5 + 49x + x2 = 0 + 217.5 Combine like terms: -217.5 + 217.5 = 0.0 0.0 + 49x + x2 = 0 + 217.5 49x + x2 = 0 + 217.5 Combine like terms: 0 + 217.5 = 217.5 49x + x2 = 217.5 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = 217.5 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 217.5 + 600.25 Combine like terms: 217.5 + 600.25 = 817.75 600.25 + 49x + x2 = 817.75 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 817.75 Calculate the square root of the right side: 28.596328436 Break this problem into two subproblems by setting (x + 24.5) equal to 28.596328436 and -28.596328436.Subproblem 1
x + 24.5 = 28.596328436 Simplifying x + 24.5 = 28.596328436 Reorder the terms: 24.5 + x = 28.596328436 Solving 24.5 + x = 28.596328436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 28.596328436 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 28.596328436 + -24.5 x = 28.596328436 + -24.5 Combine like terms: 28.596328436 + -24.5 = 4.096328436 x = 4.096328436 Simplifying x = 4.096328436Subproblem 2
x + 24.5 = -28.596328436 Simplifying x + 24.5 = -28.596328436 Reorder the terms: 24.5 + x = -28.596328436 Solving 24.5 + x = -28.596328436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -28.596328436 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -28.596328436 + -24.5 x = -28.596328436 + -24.5 Combine like terms: -28.596328436 + -24.5 = -53.096328436 x = -53.096328436 Simplifying x = -53.096328436Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.096328436, -53.096328436}
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