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Simplifying (x + 27)(x + 27) = 50 Reorder the terms: (27 + x)(x + 27) = 50 Reorder the terms: (27 + x)(27 + x) = 50 Multiply (27 + x) * (27 + x) (27(27 + x) + x(27 + x)) = 50 ((27 * 27 + x * 27) + x(27 + x)) = 50 ((729 + 27x) + x(27 + x)) = 50 (729 + 27x + (27 * x + x * x)) = 50 (729 + 27x + (27x + x2)) = 50 Combine like terms: 27x + 27x = 54x (729 + 54x + x2) = 50 Solving 729 + 54x + x2 = 50 Solving for variable 'x'. Reorder the terms: 729 + -50 + 54x + x2 = 50 + -50 Combine like terms: 729 + -50 = 679 679 + 54x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 679 + 54x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-679' to each side of the equation. 679 + 54x + -679 + x2 = 0 + -679 Reorder the terms: 679 + -679 + 54x + x2 = 0 + -679 Combine like terms: 679 + -679 = 0 0 + 54x + x2 = 0 + -679 54x + x2 = 0 + -679 Combine like terms: 0 + -679 = -679 54x + x2 = -679 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = -679 + 729 Reorder the terms: 729 + 54x + x2 = -679 + 729 Combine like terms: -679 + 729 = 50 729 + 54x + x2 = 50 Factor a perfect square on the left side: (x + 27)(x + 27) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 27) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 27 = 7.071067812 Simplifying x + 27 = 7.071067812 Reorder the terms: 27 + x = 7.071067812 Solving 27 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 7.071067812 + -27 Combine like terms: 27 + -27 = 0 0 + x = 7.071067812 + -27 x = 7.071067812 + -27 Combine like terms: 7.071067812 + -27 = -19.928932188 x = -19.928932188 Simplifying x = -19.928932188Subproblem 2
x + 27 = -7.071067812 Simplifying x + 27 = -7.071067812 Reorder the terms: 27 + x = -7.071067812 Solving 27 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -7.071067812 + -27 Combine like terms: 27 + -27 = 0 0 + x = -7.071067812 + -27 x = -7.071067812 + -27 Combine like terms: -7.071067812 + -27 = -34.071067812 x = -34.071067812 Simplifying x = -34.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {-19.928932188, -34.071067812}
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