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Simplifying x(28 + x) = 107.59 (28 * x + x * x) = 107.59 (28x + x2) = 107.59 Solving 28x + x2 = 107.59 Solving for variable 'x'. Reorder the terms: -107.59 + 28x + x2 = 107.59 + -107.59 Combine like terms: 107.59 + -107.59 = 0.00 -107.59 + 28x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '107.59' to each side of the equation. -107.59 + 28x + 107.59 + x2 = 0.00 + 107.59 Reorder the terms: -107.59 + 107.59 + 28x + x2 = 0.00 + 107.59 Combine like terms: -107.59 + 107.59 = 0.00 0.00 + 28x + x2 = 0.00 + 107.59 28x + x2 = 0.00 + 107.59 Combine like terms: 0.00 + 107.59 = 107.59 28x + x2 = 107.59 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 = 107.59 + 196 Reorder the terms: 196 + 28x + x2 = 107.59 + 196 Combine like terms: 107.59 + 196 = 303.59 196 + 28x + x2 = 303.59 Factor a perfect square on the left side: (x + 14)(x + 14) = 303.59 Calculate the square root of the right side: 17.423834251 Break this problem into two subproblems by setting (x + 14) equal to 17.423834251 and -17.423834251.Subproblem 1
x + 14 = 17.423834251 Simplifying x + 14 = 17.423834251 Reorder the terms: 14 + x = 17.423834251 Solving 14 + x = 17.423834251 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 = 17.423834251 + -14 Combine like terms: 14 + -14 = 0 0 + x = 17.423834251 + -14 x = 17.423834251 + -14 Combine like terms: 17.423834251 + -14 = 3.423834251 x = 3.423834251 Simplifying x = 3.423834251Subproblem 2
x + 14 = -17.423834251 Simplifying x + 14 = -17.423834251 Reorder the terms: 14 + x = -17.423834251 Solving 14 + x = -17.423834251 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 = -17.423834251 + -14 Combine like terms: 14 + -14 = 0 0 + x = -17.423834251 + -14 x = -17.423834251 + -14 Combine like terms: -17.423834251 + -14 = -31.423834251 x = -31.423834251 Simplifying x = -31.423834251Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.423834251, -31.423834251}
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