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Simplifying (X + 2)(X + -3) = 72 Reorder the terms: (2 + X)(X + -3) = 72 Reorder the terms: (2 + X)(-3 + X) = 72 Multiply (2 + X) * (-3 + X) (2(-3 + X) + X(-3 + X)) = 72 ((-3 * 2 + X * 2) + X(-3 + X)) = 72 ((-6 + 2X) + X(-3 + X)) = 72 (-6 + 2X + (-3 * X + X * X)) = 72 (-6 + 2X + (-3X + X2)) = 72 Combine like terms: 2X + -3X = -1X (-6 + -1X + X2) = 72 Solving -6 + -1X + X2 = 72 Solving for variable 'X'. Reorder the terms: -6 + -72 + -1X + X2 = 72 + -72 Combine like terms: -6 + -72 = -78 -78 + -1X + X2 = 72 + -72 Combine like terms: 72 + -72 = 0 -78 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -1X + 78 + X2 = 0 + 78 Reorder the terms: -78 + 78 + -1X + X2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -1X + X2 = 0 + 78 -1X + X2 = 0 + 78 Combine like terms: 0 + 78 = 78 -1X + X2 = 78 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 78 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 78 + 0.25 Combine like terms: 78 + 0.25 = 78.25 0.25 + -1X + X2 = 78.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (X + -0.5) equal to 8.845903006 and -8.845903006.Subproblem 1
X + -0.5 = 8.845903006 Simplifying X + -0.5 = 8.845903006 Reorder the terms: -0.5 + X = 8.845903006 Solving -0.5 + X = 8.845903006 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 8.845903006 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 8.845903006 + 0.5 X = 8.845903006 + 0.5 Combine like terms: 8.845903006 + 0.5 = 9.345903006 X = 9.345903006 Simplifying X = 9.345903006Subproblem 2
X + -0.5 = -8.845903006 Simplifying X + -0.5 = -8.845903006 Reorder the terms: -0.5 + X = -8.845903006 Solving -0.5 + X = -8.845903006 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -8.845903006 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -8.845903006 + 0.5 X = -8.845903006 + 0.5 Combine like terms: -8.845903006 + 0.5 = -8.345903006 X = -8.345903006 Simplifying X = -8.345903006Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.345903006, -8.345903006}
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