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