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Simplifying (x + -5)(x + -5) = 48 Reorder the terms: (-5 + x)(x + -5) = 48 Reorder the terms: (-5 + x)(-5 + x) = 48 Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x)) = 48 ((-5 * -5 + x * -5) + x(-5 + x)) = 48 ((25 + -5x) + x(-5 + x)) = 48 (25 + -5x + (-5 * x + x * x)) = 48 (25 + -5x + (-5x + x2)) = 48 Combine like terms: -5x + -5x = -10x (25 + -10x + x2) = 48 Solving 25 + -10x + x2 = 48 Solving for variable 'x'. Reorder the terms: 25 + -48 + -10x + x2 = 48 + -48 Combine like terms: 25 + -48 = -23 -23 + -10x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -23 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -10x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -10x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -10x + x2 = 0 + 23 -10x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -10x + x2 = 23 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 23 + 25 Reorder the terms: 25 + -10x + x2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + -10x + x2 = 48 Factor a perfect square on the left side: (x + -5)(x + -5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -5) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -5 = 6.92820323 Simplifying x + -5 = 6.92820323 Reorder the terms: -5 + x = 6.92820323 Solving -5 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.92820323 + 5 x = 6.92820323 + 5 Combine like terms: 6.92820323 + 5 = 11.92820323 x = 11.92820323 Simplifying x = 11.92820323Subproblem 2
x + -5 = -6.92820323 Simplifying x + -5 = -6.92820323 Reorder the terms: -5 + x = -6.92820323 Solving -5 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.92820323 + 5 x = -6.92820323 + 5 Combine like terms: -6.92820323 + 5 = -1.92820323 x = -1.92820323 Simplifying x = -1.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.92820323, -1.92820323}
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