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Simplifying (x2) + -72x + 7 = 0 x2 + -72x + 7 = 0 Reorder the terms: 7 + -72x + x2 = 0 Solving 7 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -72x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -72x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -72x + x2 = 0 + -7 -72x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -72x + x2 = -7 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 = -7 + 1296 Reorder the terms: 1296 + -72x + x2 = -7 + 1296 Combine like terms: -7 + 1296 = 1289 1296 + -72x + x2 = 1289 Factor a perfect square on the left side: (x + -36)(x + -36) = 1289 Calculate the square root of the right side: 35.902646142 Break this problem into two subproblems by setting (x + -36) equal to 35.902646142 and -35.902646142.Subproblem 1
x + -36 = 35.902646142 Simplifying x + -36 = 35.902646142 Reorder the terms: -36 + x = 35.902646142 Solving -36 + x = 35.902646142 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 = 35.902646142 + 36 Combine like terms: -36 + 36 = 0 0 + x = 35.902646142 + 36 x = 35.902646142 + 36 Combine like terms: 35.902646142 + 36 = 71.902646142 x = 71.902646142 Simplifying x = 71.902646142Subproblem 2
x + -36 = -35.902646142 Simplifying x + -36 = -35.902646142 Reorder the terms: -36 + x = -35.902646142 Solving -36 + x = -35.902646142 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 = -35.902646142 + 36 Combine like terms: -36 + 36 = 0 0 + x = -35.902646142 + 36 x = -35.902646142 + 36 Combine like terms: -35.902646142 + 36 = 0.097353858 x = 0.097353858 Simplifying x = 0.097353858Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.902646142, 0.097353858}
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