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Simplifying 0.25x2 = 0.5x + 2 Reorder the terms: 0.25x2 = 2 + 0.5x Solving 0.25x2 = 2 + 0.5x Solving for variable 'x'. Reorder the terms: -2 + -0.5x + 0.25x2 = 2 + 0.5x + -2 + -0.5x Reorder the terms: -2 + -0.5x + 0.25x2 = 2 + -2 + 0.5x + -0.5x Combine like terms: 2 + -2 = 0 -2 + -0.5x + 0.25x2 = 0 + 0.5x + -0.5x -2 + -0.5x + 0.25x2 = 0.5x + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 -2 + -0.5x + 0.25x2 = 0.0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -8 + -2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2x + x2 = 0 + 8 -2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2x + x2 = 8 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 8 + 1 Reorder the terms: 1 + -2x + x2 = 8 + 1 Combine like terms: 8 + 1 = 9 1 + -2x + x2 = 9 Factor a perfect square on the left side: (x + -1)(x + -1) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -1) equal to 3 and -3.Subproblem 1
x + -1 = 3 Simplifying x + -1 = 3 Reorder the terms: -1 + x = 3 Solving -1 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3 + 1 x = 3 + 1 Combine like terms: 3 + 1 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -1 = -3 Simplifying x + -1 = -3 Reorder the terms: -1 + x = -3 Solving -1 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3 + 1 x = -3 + 1 Combine like terms: -3 + 1 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -2}
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