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Simplifying -1x + 8 = 4x + -0.5x2 Reorder the terms: 8 + -1x = 4x + -0.5x2 Solving 8 + -1x = 4x + -0.5x2 Solving for variable 'x'. Combine like terms: -1x + -4x = -5x 8 + -5x + 0.5x2 = 4x + -0.5x2 + -4x + 0.5x2 Reorder the terms: 8 + -5x + 0.5x2 = 4x + -4x + -0.5x2 + 0.5x2 Combine like terms: 4x + -4x = 0 8 + -5x + 0.5x2 = 0 + -0.5x2 + 0.5x2 8 + -5x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 8 + -5x + 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'. 16 + -10x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -10x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -10x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -10x + x2 = 0 + -16 -10x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -10x + x2 = -16 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -16 + 25 Reorder the terms: 25 + -10x + x2 = -16 + 25 Combine like terms: -16 + 25 = 9 25 + -10x + x2 = 9 Factor a perfect square on the left side: (x + -5)(x + -5) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -5) equal to 3 and -3.Subproblem 1
x + -5 = 3 Simplifying x + -5 = 3 Reorder the terms: -5 + x = 3 Solving -5 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3 + 5 x = 3 + 5 Combine like terms: 3 + 5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -5 = -3 Simplifying x + -5 = -3 Reorder the terms: -5 + x = -3 Solving -5 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3 + 5 x = -3 + 5 Combine like terms: -3 + 5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 2}
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