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Simplifying x2 + -2x + -72 = 0 Reorder the terms: -72 + -2x + x2 = 0 Solving -72 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -2x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -2x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -2x + x2 = 0 + 72 -2x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -2x + x2 = 72 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 72 + 1 Reorder the terms: 1 + -2x + x2 = 72 + 1 Combine like terms: 72 + 1 = 73 1 + -2x + x2 = 73 Factor a perfect square on the left side: (x + -1)(x + -1) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + -1) equal to 8.544003745 and -8.544003745.Subproblem 1
x + -1 = 8.544003745 Simplifying x + -1 = 8.544003745 Reorder the terms: -1 + x = 8.544003745 Solving -1 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.544003745 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.544003745 + 1 x = 8.544003745 + 1 Combine like terms: 8.544003745 + 1 = 9.544003745 x = 9.544003745 Simplifying x = 9.544003745Subproblem 2
x + -1 = -8.544003745 Simplifying x + -1 = -8.544003745 Reorder the terms: -1 + x = -8.544003745 Solving -1 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.544003745 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.544003745 + 1 x = -8.544003745 + 1 Combine like terms: -8.544003745 + 1 = -7.544003745 x = -7.544003745 Simplifying x = -7.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.544003745, -7.544003745}
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