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Simplifying x2 + 4x = 73 Reorder the terms: 4x + x2 = 73 Solving 4x + x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 4x + x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 4x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 4x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 4x + x2 = 0 + 73 4x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 4x + x2 = 73 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 = 73 + 4 Reorder the terms: 4 + 4x + x2 = 73 + 4 Combine like terms: 73 + 4 = 77 4 + 4x + x2 = 77 Factor a perfect square on the left side: (x + 2)(x + 2) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 2) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 2 = 8.774964387 Simplifying x + 2 = 8.774964387 Reorder the terms: 2 + x = 8.774964387 Solving 2 + x = 8.774964387 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 = 8.774964387 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.774964387 + -2 x = 8.774964387 + -2 Combine like terms: 8.774964387 + -2 = 6.774964387 x = 6.774964387 Simplifying x = 6.774964387Subproblem 2
x + 2 = -8.774964387 Simplifying x + 2 = -8.774964387 Reorder the terms: 2 + x = -8.774964387 Solving 2 + x = -8.774964387 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 = -8.774964387 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.774964387 + -2 x = -8.774964387 + -2 Combine like terms: -8.774964387 + -2 = -10.774964387 x = -10.774964387 Simplifying x = -10.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.774964387, -10.774964387}
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