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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 = 216 144 + 24X + X2 = 216 Factor a perfect square on the left side: (X + 12)(X + 12) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (X + 12) equal to 14.696938457 and -14.696938457.Subproblem 1
X + 12 = 14.696938457 Simplifying X + 12 = 14.696938457 Reorder the terms: 12 + X = 14.696938457 Solving 12 + X = 14.696938457 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 = 14.696938457 + -12 Combine like terms: 12 + -12 = 0 0 + X = 14.696938457 + -12 X = 14.696938457 + -12 Combine like terms: 14.696938457 + -12 = 2.696938457 X = 2.696938457 Simplifying X = 2.696938457Subproblem 2
X + 12 = -14.696938457 Simplifying X + 12 = -14.696938457 Reorder the terms: 12 + X = -14.696938457 Solving 12 + X = -14.696938457 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 = -14.696938457 + -12 Combine like terms: 12 + -12 = 0 0 + X = -14.696938457 + -12 X = -14.696938457 + -12 Combine like terms: -14.696938457 + -12 = -26.696938457 X = -26.696938457 Simplifying X = -26.696938457Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.696938457, -26.696938457}
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