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Simplifying 3x = 0.5x2 + 2.5 Reorder the terms: 3x = 2.5 + 0.5x2 Solving 3x = 2.5 + 0.5x2 Solving for variable 'x'. Reorder the terms: -2.5 + 3x + -0.5x2 = 2.5 + 0.5x2 + -2.5 + -0.5x2 Reorder the terms: -2.5 + 3x + -0.5x2 = 2.5 + -2.5 + 0.5x2 + -0.5x2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + 3x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 -2.5 + 3x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -2.5 + 3x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 5 + -6x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -6x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x + x2 = 0 + -5 -6x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6x + x2 = -5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5 + 9 Reorder the terms: 9 + -6x + x2 = -5 + 9 Combine like terms: -5 + 9 = 4 9 + -6x + x2 = 4 Factor a perfect square on the left side: (x + -3)(x + -3) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + -3) equal to 2 and -2.Subproblem 1
x + -3 = 2 Simplifying x + -3 = 2 Reorder the terms: -3 + x = 2 Solving -3 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2 + 3 x = 2 + 3 Combine like terms: 2 + 3 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -3 = -2 Simplifying x + -3 = -2 Reorder the terms: -3 + x = -2 Solving -3 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2 + 3 x = -2 + 3 Combine like terms: -2 + 3 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 1}
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