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Simplifying x2 + -72x + 60 = 0 Reorder the terms: 60 + -72x + x2 = 0 Solving 60 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -72x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -72x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -72x + x2 = 0 + -60 -72x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -72x + x2 = -60 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 = -60 + 1296 Reorder the terms: 1296 + -72x + x2 = -60 + 1296 Combine like terms: -60 + 1296 = 1236 1296 + -72x + x2 = 1236 Factor a perfect square on the left side: (x + -36)(x + -36) = 1236 Calculate the square root of the right side: 35.156791662 Break this problem into two subproblems by setting (x + -36) equal to 35.156791662 and -35.156791662.Subproblem 1
x + -36 = 35.156791662 Simplifying x + -36 = 35.156791662 Reorder the terms: -36 + x = 35.156791662 Solving -36 + x = 35.156791662 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 = 35.156791662 + 36 Combine like terms: -36 + 36 = 0 0 + x = 35.156791662 + 36 x = 35.156791662 + 36 Combine like terms: 35.156791662 + 36 = 71.156791662 x = 71.156791662 Simplifying x = 71.156791662Subproblem 2
x + -36 = -35.156791662 Simplifying x + -36 = -35.156791662 Reorder the terms: -36 + x = -35.156791662 Solving -36 + x = -35.156791662 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 = -35.156791662 + 36 Combine like terms: -36 + 36 = 0 0 + x = -35.156791662 + 36 x = -35.156791662 + 36 Combine like terms: -35.156791662 + 36 = 0.843208338 x = 0.843208338 Simplifying x = 0.843208338Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.156791662, 0.843208338}
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