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Simplifying (x + 4) * x = 28 Reorder the terms: (4 + x) * x = 28 Reorder the terms for easier multiplication: x(4 + x) = 28 (4 * x + x * x) = 28 (4x + x2) = 28 Solving 4x + x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 4x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 4x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 4x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 4x + x2 = 0 + 28 4x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 4x + x2 = 28 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 = 28 + 4 Reorder the terms: 4 + 4x + x2 = 28 + 4 Combine like terms: 28 + 4 = 32 4 + 4x + x2 = 32 Factor a perfect square on the left side: (x + 2)(x + 2) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 2) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 2 = 5.656854249 Simplifying x + 2 = 5.656854249 Reorder the terms: 2 + x = 5.656854249 Solving 2 + x = 5.656854249 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 = 5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.656854249 + -2 x = 5.656854249 + -2 Combine like terms: 5.656854249 + -2 = 3.656854249 x = 3.656854249 Simplifying x = 3.656854249Subproblem 2
x + 2 = -5.656854249 Simplifying x + 2 = -5.656854249 Reorder the terms: 2 + x = -5.656854249 Solving 2 + x = -5.656854249 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 = -5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.656854249 + -2 x = -5.656854249 + -2 Combine like terms: -5.656854249 + -2 = -7.656854249 x = -7.656854249 Simplifying x = -7.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.656854249, -7.656854249}
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