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Simplifying x2 + -24x + 72 = 0 Reorder the terms: 72 + -24x + x2 = 0 Solving 72 + -24x + 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 + -24x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -24x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -24x + x2 = 0 + -72 -24x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -24x + x2 = -72 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -72 + 144 Reorder the terms: 144 + -24x + x2 = -72 + 144 Combine like terms: -72 + 144 = 72 144 + -24x + x2 = 72 Factor a perfect square on the left side: (x + -12)(x + -12) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -12) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -12 = 8.485281374 Simplifying x + -12 = 8.485281374 Reorder the terms: -12 + x = 8.485281374 Solving -12 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 8.485281374 + 12 Combine like terms: -12 + 12 = 0 0 + x = 8.485281374 + 12 x = 8.485281374 + 12 Combine like terms: 8.485281374 + 12 = 20.485281374 x = 20.485281374 Simplifying x = 20.485281374Subproblem 2
x + -12 = -8.485281374 Simplifying x + -12 = -8.485281374 Reorder the terms: -12 + x = -8.485281374 Solving -12 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -8.485281374 + 12 Combine like terms: -12 + 12 = 0 0 + x = -8.485281374 + 12 x = -8.485281374 + 12 Combine like terms: -8.485281374 + 12 = 3.514718626 x = 3.514718626 Simplifying x = 3.514718626Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.485281374, 3.514718626}
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