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Simplifying (x + 7)(x + 7) + 4 = 52 Reorder the terms: (7 + x)(x + 7) + 4 = 52 Reorder the terms: (7 + x)(7 + x) + 4 = 52 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) + 4 = 52 ((7 * 7 + x * 7) + x(7 + x)) + 4 = 52 ((49 + 7x) + x(7 + x)) + 4 = 52 (49 + 7x + (7 * x + x * x)) + 4 = 52 (49 + 7x + (7x + x2)) + 4 = 52 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) + 4 = 52 Reorder the terms: 49 + 4 + 14x + x2 = 52 Combine like terms: 49 + 4 = 53 53 + 14x + x2 = 52 Solving 53 + 14x + x2 = 52 Solving for variable 'x'. Reorder the terms: 53 + -52 + 14x + x2 = 52 + -52 Combine like terms: 53 + -52 = 1 1 + 14x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 1 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 14x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 14x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 14x + x2 = 0 + -1 14x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 14x + x2 = -1 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -1 + 49 Reorder the terms: 49 + 14x + x2 = -1 + 49 Combine like terms: -1 + 49 = 48 49 + 14x + x2 = 48 Factor a perfect square on the left side: (x + 7)(x + 7) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 7) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 7 = 6.92820323 Simplifying x + 7 = 6.92820323 Reorder the terms: 7 + x = 6.92820323 Solving 7 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 6.92820323 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.92820323 + -7 x = 6.92820323 + -7 Combine like terms: 6.92820323 + -7 = -0.07179677 x = -0.07179677 Simplifying x = -0.07179677Subproblem 2
x + 7 = -6.92820323 Simplifying x + 7 = -6.92820323 Reorder the terms: 7 + x = -6.92820323 Solving 7 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -6.92820323 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.92820323 + -7 x = -6.92820323 + -7 Combine like terms: -6.92820323 + -7 = -13.92820323 x = -13.92820323 Simplifying x = -13.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.07179677, -13.92820323}
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