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Simplifying X = 4X2 + -24X + -36 Reorder the terms: X = -36 + -24X + 4X2 Solving X = -36 + -24X + 4X2 Solving for variable 'X'. Reorder the terms: 36 + X + 24X + -4X2 = -36 + -24X + 4X2 + 36 + 24X + -4X2 Combine like terms: X + 24X = 25X 36 + 25X + -4X2 = -36 + -24X + 4X2 + 36 + 24X + -4X2 Reorder the terms: 36 + 25X + -4X2 = -36 + 36 + -24X + 24X + 4X2 + -4X2 Combine like terms: -36 + 36 = 0 36 + 25X + -4X2 = 0 + -24X + 24X + 4X2 + -4X2 36 + 25X + -4X2 = -24X + 24X + 4X2 + -4X2 Combine like terms: -24X + 24X = 0 36 + 25X + -4X2 = 0 + 4X2 + -4X2 36 + 25X + -4X2 = 4X2 + -4X2 Combine like terms: 4X2 + -4X2 = 0 36 + 25X + -4X2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9 + -6.25X + X2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -6.25X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + -6.25X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6.25X + X2 = 0 + 9 -6.25X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6.25X + X2 = 9 The X term is -6.25X. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25X + 9.765625 + X2 = 9 + 9.765625 Reorder the terms: 9.765625 + -6.25X + X2 = 9 + 9.765625 Combine like terms: 9 + 9.765625 = 18.765625 9.765625 + -6.25X + X2 = 18.765625 Factor a perfect square on the left side: (X + -3.125)(X + -3.125) = 18.765625 Calculate the square root of the right side: 4.331930863 Break this problem into two subproblems by setting (X + -3.125) equal to 4.331930863 and -4.331930863.Subproblem 1
X + -3.125 = 4.331930863 Simplifying X + -3.125 = 4.331930863 Reorder the terms: -3.125 + X = 4.331930863 Solving -3.125 + X = 4.331930863 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + X = 4.331930863 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + X = 4.331930863 + 3.125 X = 4.331930863 + 3.125 Combine like terms: 4.331930863 + 3.125 = 7.456930863 X = 7.456930863 Simplifying X = 7.456930863Subproblem 2
X + -3.125 = -4.331930863 Simplifying X + -3.125 = -4.331930863 Reorder the terms: -3.125 + X = -4.331930863 Solving -3.125 + X = -4.331930863 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + X = -4.331930863 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + X = -4.331930863 + 3.125 X = -4.331930863 + 3.125 Combine like terms: -4.331930863 + 3.125 = -1.206930863 X = -1.206930863 Simplifying X = -1.206930863Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.456930863, -1.206930863}
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