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Simplifying 936 = 2X2 + 8X Reorder the terms: 936 = 8X + 2X2 Solving 936 = 8X + 2X2 Solving for variable 'X'. Reorder the terms: 936 + -8X + -2X2 = 8X + -8X + 2X2 + -2X2 Combine like terms: 8X + -8X = 0 936 + -8X + -2X2 = 0 + 2X2 + -2X2 936 + -8X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 936 + -8X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(468 + -4X + -1X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(468 + -4X + -1X2)' equal to zero and attempt to solve: Simplifying 468 + -4X + -1X2 = 0 Solving 468 + -4X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -468 + 4X + X2 = 0 Move the constant term to the right: Add '468' to each side of the equation. -468 + 4X + 468 + X2 = 0 + 468 Reorder the terms: -468 + 468 + 4X + X2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + 4X + X2 = 0 + 468 4X + X2 = 0 + 468 Combine like terms: 0 + 468 = 468 4X + X2 = 468 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 468 + 4 Reorder the terms: 4 + 4X + X2 = 468 + 4 Combine like terms: 468 + 4 = 472 4 + 4X + X2 = 472 Factor a perfect square on the left side: (X + 2)(X + 2) = 472 Calculate the square root of the right side: 21.725560982 Break this problem into two subproblems by setting (X + 2) equal to 21.725560982 and -21.725560982.Subproblem 1
X + 2 = 21.725560982 Simplifying X + 2 = 21.725560982 Reorder the terms: 2 + X = 21.725560982 Solving 2 + X = 21.725560982 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 21.725560982 + -2 Combine like terms: 2 + -2 = 0 0 + X = 21.725560982 + -2 X = 21.725560982 + -2 Combine like terms: 21.725560982 + -2 = 19.725560982 X = 19.725560982 Simplifying X = 19.725560982Subproblem 2
X + 2 = -21.725560982 Simplifying X + 2 = -21.725560982 Reorder the terms: 2 + X = -21.725560982 Solving 2 + X = -21.725560982 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -21.725560982 + -2 Combine like terms: 2 + -2 = 0 0 + X = -21.725560982 + -2 X = -21.725560982 + -2 Combine like terms: -21.725560982 + -2 = -23.725560982 X = -23.725560982 Simplifying X = -23.725560982Solution
The solution to the problem is based on the solutions from the subproblems. X = {19.725560982, -23.725560982}Solution
X = {19.725560982, -23.725560982}
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