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Simplifying x2 + -72x + -144 = 0 Reorder the terms: -144 + -72x + x2 = 0 Solving -144 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -72x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -72x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -72x + x2 = 0 + 144 -72x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -72x + x2 = 144 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = 144 + 1296 Reorder the terms: 1296 + -72x + x2 = 144 + 1296 Combine like terms: 144 + 1296 = 1440 1296 + -72x + x2 = 1440 Factor a perfect square on the left side: (x + -36)(x + -36) = 1440 Calculate the square root of the right side: 37.947331922 Break this problem into two subproblems by setting (x + -36) equal to 37.947331922 and -37.947331922.Subproblem 1
x + -36 = 37.947331922 Simplifying x + -36 = 37.947331922 Reorder the terms: -36 + x = 37.947331922 Solving -36 + x = 37.947331922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 37.947331922 + 36 Combine like terms: -36 + 36 = 0 0 + x = 37.947331922 + 36 x = 37.947331922 + 36 Combine like terms: 37.947331922 + 36 = 73.947331922 x = 73.947331922 Simplifying x = 73.947331922Subproblem 2
x + -36 = -37.947331922 Simplifying x + -36 = -37.947331922 Reorder the terms: -36 + x = -37.947331922 Solving -36 + x = -37.947331922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -37.947331922 + 36 Combine like terms: -36 + 36 = 0 0 + x = -37.947331922 + 36 x = -37.947331922 + 36 Combine like terms: -37.947331922 + 36 = -1.947331922 x = -1.947331922 Simplifying x = -1.947331922Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.947331922, -1.947331922}
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