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Simplifying 8 + -1(X + -2)(X + -3) = 0solve Reorder the terms: 8 + -1(-2 + X)(X + -3) = 0solve Reorder the terms: 8 + -1(-2 + X)(-3 + X) = 0solve Multiply (-2 + X) * (-3 + X) 8 + -1(-2(-3 + X) + X(-3 + X)) = 0solve 8 + -1((-3 * -2 + X * -2) + X(-3 + X)) = 0solve 8 + -1((6 + -2X) + X(-3 + X)) = 0solve 8 + -1(6 + -2X + (-3 * X + X * X)) = 0solve 8 + -1(6 + -2X + (-3X + X2)) = 0solve Combine like terms: -2X + -3X = -5X 8 + -1(6 + -5X + X2) = 0solve 8 + (6 * -1 + -5X * -1 + X2 * -1) = 0solve 8 + (-6 + 5X + -1X2) = 0solve Combine like terms: 8 + -6 = 2 2 + 5X + -1X2 = 0solve Anything times zero is zero. 2 + 5X + -1X2 = 0elosv Solving 2 + 5X + -1X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -5X + X2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5X + 2 + X2 = 0 + 2 Reorder the terms: -2 + 2 + -5X + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5X + X2 = 0 + 2 -5X + X2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5X + X2 = 2 The X term is -5X. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5X + 6.25 + X2 = 2 + 6.25 Reorder the terms: 6.25 + -5X + X2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5X + X2 = 8.25 Factor a perfect square on the left side: (X + -2.5)(X + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (X + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
X + -2.5 = 2.872281323 Simplifying X + -2.5 = 2.872281323 Reorder the terms: -2.5 + X = 2.872281323 Solving -2.5 + X = 2.872281323 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = 2.872281323 + 2.5 X = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 X = 5.372281323 Simplifying X = 5.372281323Subproblem 2
X + -2.5 = -2.872281323 Simplifying X + -2.5 = -2.872281323 Reorder the terms: -2.5 + X = -2.872281323 Solving -2.5 + X = -2.872281323 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = -2.872281323 + 2.5 X = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 X = -0.372281323 Simplifying X = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.372281323, -0.372281323}
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