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Simplifying 5X2 + 4X = 2X + 12 Reorder the terms: 4X + 5X2 = 2X + 12 Reorder the terms: 4X + 5X2 = 12 + 2X Solving 4X + 5X2 = 12 + 2X Solving for variable 'X'. Reorder the terms: -12 + 4X + -2X + 5X2 = 12 + 2X + -12 + -2X Combine like terms: 4X + -2X = 2X -12 + 2X + 5X2 = 12 + 2X + -12 + -2X Reorder the terms: -12 + 2X + 5X2 = 12 + -12 + 2X + -2X Combine like terms: 12 + -12 = 0 -12 + 2X + 5X2 = 0 + 2X + -2X -12 + 2X + 5X2 = 2X + -2X Combine like terms: 2X + -2X = 0 -12 + 2X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 0.4X + X2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.4X + 2.4 + X2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.4X + X2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.4X + X2 = 0 + 2.4 0.4X + X2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.4X + X2 = 2.4 The X term is 0.4X. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4X + 0.04 + X2 = 2.4 + 0.04 Reorder the terms: 0.04 + 0.4X + X2 = 2.4 + 0.04 Combine like terms: 2.4 + 0.04 = 2.44 0.04 + 0.4X + X2 = 2.44 Factor a perfect square on the left side: (X + 0.2)(X + 0.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (X + 0.2) equal to 1.562049935 and -1.562049935.Subproblem 1
X + 0.2 = 1.562049935 Simplifying X + 0.2 = 1.562049935 Reorder the terms: 0.2 + X = 1.562049935 Solving 0.2 + X = 1.562049935 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + X = 1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + X = 1.562049935 + -0.2 X = 1.562049935 + -0.2 Combine like terms: 1.562049935 + -0.2 = 1.362049935 X = 1.362049935 Simplifying X = 1.362049935Subproblem 2
X + 0.2 = -1.562049935 Simplifying X + 0.2 = -1.562049935 Reorder the terms: 0.2 + X = -1.562049935 Solving 0.2 + X = -1.562049935 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + X = -1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + X = -1.562049935 + -0.2 X = -1.562049935 + -0.2 Combine like terms: -1.562049935 + -0.2 = -1.762049935 X = -1.762049935 Simplifying X = -1.762049935Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.362049935, -1.762049935}
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