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Simplifying x2 + 121(x + -5) + -5184 = 0 Reorder the terms: x2 + 121(-5 + x) + -5184 = 0 x2 + (-5 * 121 + x * 121) + -5184 = 0 x2 + (-605 + 121x) + -5184 = 0 Reorder the terms: -605 + -5184 + 121x + x2 = 0 Combine like terms: -605 + -5184 = -5789 -5789 + 121x + x2 = 0 Solving -5789 + 121x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5789' to each side of the equation. -5789 + 121x + 5789 + x2 = 0 + 5789 Reorder the terms: -5789 + 5789 + 121x + x2 = 0 + 5789 Combine like terms: -5789 + 5789 = 0 0 + 121x + x2 = 0 + 5789 121x + x2 = 0 + 5789 Combine like terms: 0 + 5789 = 5789 121x + x2 = 5789 The x term is 121x. Take half its coefficient (60.5). Square it (3660.25) and add it to both sides. Add '3660.25' to each side of the equation. 121x + 3660.25 + x2 = 5789 + 3660.25 Reorder the terms: 3660.25 + 121x + x2 = 5789 + 3660.25 Combine like terms: 5789 + 3660.25 = 9449.25 3660.25 + 121x + x2 = 9449.25 Factor a perfect square on the left side: (x + 60.5)(x + 60.5) = 9449.25 Calculate the square root of the right side: 97.207252816 Break this problem into two subproblems by setting (x + 60.5) equal to 97.207252816 and -97.207252816.Subproblem 1
x + 60.5 = 97.207252816 Simplifying x + 60.5 = 97.207252816 Reorder the terms: 60.5 + x = 97.207252816 Solving 60.5 + x = 97.207252816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + x = 97.207252816 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + x = 97.207252816 + -60.5 x = 97.207252816 + -60.5 Combine like terms: 97.207252816 + -60.5 = 36.707252816 x = 36.707252816 Simplifying x = 36.707252816Subproblem 2
x + 60.5 = -97.207252816 Simplifying x + 60.5 = -97.207252816 Reorder the terms: 60.5 + x = -97.207252816 Solving 60.5 + x = -97.207252816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + x = -97.207252816 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + x = -97.207252816 + -60.5 x = -97.207252816 + -60.5 Combine like terms: -97.207252816 + -60.5 = -157.707252816 x = -157.707252816 Simplifying x = -157.707252816Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.707252816, -157.707252816}
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