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Simplifying -5X + 12 = 5X2 + -12 Reorder the terms: 12 + -5X = 5X2 + -12 Reorder the terms: 12 + -5X = -12 + 5X2 Solving 12 + -5X = -12 + 5X2 Solving for variable 'X'. Reorder the terms: 12 + 12 + -5X + -5X2 = -12 + 5X2 + 12 + -5X2 Combine like terms: 12 + 12 = 24 24 + -5X + -5X2 = -12 + 5X2 + 12 + -5X2 Reorder the terms: 24 + -5X + -5X2 = -12 + 12 + 5X2 + -5X2 Combine like terms: -12 + 12 = 0 24 + -5X + -5X2 = 0 + 5X2 + -5X2 24 + -5X + -5X2 = 5X2 + -5X2 Combine like terms: 5X2 + -5X2 = 0 24 + -5X + -5X2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.8 + X + X2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + X + 4.8 + X2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + X + X2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + X + X2 = 0 + 4.8 X + X2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 X + X2 = 4.8 The X term is X. 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. + 0.25 + X2 = 4.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 4.8 + 0.25 Combine like terms: 4.8 + 0.25 = 5.05 1.25 + X2 = 5.05 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 5.05 Calculate the square root of the right side: 2.247220505 Break this problem into two subproblems by setting (X + 0.5) equal to 2.247220505 and -2.247220505.Subproblem 1
X + 0.5 = 2.247220505 Simplifying X + 0.5 = 2.247220505 Reorder the terms: 0.5 + X = 2.247220505 Solving 0.5 + X = 2.247220505 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 = 2.247220505 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 2.247220505 + -0.5 X = 2.247220505 + -0.5 Combine like terms: 2.247220505 + -0.5 = 1.747220505 X = 1.747220505 Simplifying X = 1.747220505Subproblem 2
X + 0.5 = -2.247220505 Simplifying X + 0.5 = -2.247220505 Reorder the terms: 0.5 + X = -2.247220505 Solving 0.5 + X = -2.247220505 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 = -2.247220505 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -2.247220505 + -0.5 X = -2.247220505 + -0.5 Combine like terms: -2.247220505 + -0.5 = -2.747220505 X = -2.747220505 Simplifying X = -2.747220505Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.747220505, -2.747220505}
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