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Simplifying 4x + x2 = 242 Solving 4x + x2 = 242 Solving for variable 'x'. Reorder the terms: -242 + 4x + x2 = 242 + -242 Combine like terms: 242 + -242 = 0 -242 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '242' to each side of the equation. -242 + 4x + 242 + x2 = 0 + 242 Reorder the terms: -242 + 242 + 4x + x2 = 0 + 242 Combine like terms: -242 + 242 = 0 0 + 4x + x2 = 0 + 242 4x + x2 = 0 + 242 Combine like terms: 0 + 242 = 242 4x + x2 = 242 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 242 + 4 Reorder the terms: 4 + 4x + x2 = 242 + 4 Combine like terms: 242 + 4 = 246 4 + 4x + x2 = 246 Factor a perfect square on the left side: (x + 2)(x + 2) = 246 Calculate the square root of the right side: 15.684387141 Break this problem into two subproblems by setting (x + 2) equal to 15.684387141 and -15.684387141.Subproblem 1
x + 2 = 15.684387141 Simplifying x + 2 = 15.684387141 Reorder the terms: 2 + x = 15.684387141 Solving 2 + x = 15.684387141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 15.684387141 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.684387141 + -2 x = 15.684387141 + -2 Combine like terms: 15.684387141 + -2 = 13.684387141 x = 13.684387141 Simplifying x = 13.684387141Subproblem 2
x + 2 = -15.684387141 Simplifying x + 2 = -15.684387141 Reorder the terms: 2 + x = -15.684387141 Solving 2 + x = -15.684387141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -15.684387141 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.684387141 + -2 x = -15.684387141 + -2 Combine like terms: -15.684387141 + -2 = -17.684387141 x = -17.684387141 Simplifying x = -17.684387141Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.684387141, -17.684387141}
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