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Simplifying x(x + 4) = 104 Reorder the terms: x(4 + x) = 104 (4 * x + x * x) = 104 (4x + x2) = 104 Solving 4x + x2 = 104 Solving for variable 'x'. Reorder the terms: -104 + 4x + x2 = 104 + -104 Combine like terms: 104 + -104 = 0 -104 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 4x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 4x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 4x + x2 = 0 + 104 4x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 4x + x2 = 104 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 = 104 + 4 Reorder the terms: 4 + 4x + x2 = 104 + 4 Combine like terms: 104 + 4 = 108 4 + 4x + x2 = 108 Factor a perfect square on the left side: (x + 2)(x + 2) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 2) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 2 = 10.392304845 Simplifying x + 2 = 10.392304845 Reorder the terms: 2 + x = 10.392304845 Solving 2 + x = 10.392304845 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 = 10.392304845 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.392304845 + -2 x = 10.392304845 + -2 Combine like terms: 10.392304845 + -2 = 8.392304845 x = 8.392304845 Simplifying x = 8.392304845Subproblem 2
x + 2 = -10.392304845 Simplifying x + 2 = -10.392304845 Reorder the terms: 2 + x = -10.392304845 Solving 2 + x = -10.392304845 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 = -10.392304845 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.392304845 + -2 x = -10.392304845 + -2 Combine like terms: -10.392304845 + -2 = -12.392304845 x = -12.392304845 Simplifying x = -12.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.392304845, -12.392304845}
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