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Simplifying x2 + -72x + -400 = 0 Reorder the terms: -400 + -72x + x2 = 0 Solving -400 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -72x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -72x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -72x + x2 = 0 + 400 -72x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -72x + x2 = 400 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 = 400 + 1296 Reorder the terms: 1296 + -72x + x2 = 400 + 1296 Combine like terms: 400 + 1296 = 1696 1296 + -72x + x2 = 1696 Factor a perfect square on the left side: (x + -36)(x + -36) = 1696 Calculate the square root of the right side: 41.182520564 Break this problem into two subproblems by setting (x + -36) equal to 41.182520564 and -41.182520564.Subproblem 1
x + -36 = 41.182520564 Simplifying x + -36 = 41.182520564 Reorder the terms: -36 + x = 41.182520564 Solving -36 + x = 41.182520564 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 = 41.182520564 + 36 Combine like terms: -36 + 36 = 0 0 + x = 41.182520564 + 36 x = 41.182520564 + 36 Combine like terms: 41.182520564 + 36 = 77.182520564 x = 77.182520564 Simplifying x = 77.182520564Subproblem 2
x + -36 = -41.182520564 Simplifying x + -36 = -41.182520564 Reorder the terms: -36 + x = -41.182520564 Solving -36 + x = -41.182520564 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 = -41.182520564 + 36 Combine like terms: -36 + 36 = 0 0 + x = -41.182520564 + 36 x = -41.182520564 + 36 Combine like terms: -41.182520564 + 36 = -5.182520564 x = -5.182520564 Simplifying x = -5.182520564Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.182520564, -5.182520564}
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