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Simplifying -0.5x2 + 2x + 0.5 = 0 Reorder the terms: 0.5 + 2x + -0.5x2 = 0 Solving 0.5 + 2x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -1 + -4x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x + x2 = 0 + 1 -4x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4x + x2 = 1 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 = 1 + 4 Reorder the terms: 4 + -4x + x2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4x + x2 = 5 Factor a perfect square on the left side: (x + -2)(x + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -2 = 2.236067978 Simplifying x + -2 = 2.236067978 Reorder the terms: -2 + x = 2.236067978 Solving -2 + x = 2.236067978 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 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.236067978 + 2 x = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 x = 4.236067978 Simplifying x = 4.236067978Subproblem 2
x + -2 = -2.236067978 Simplifying x + -2 = -2.236067978 Reorder the terms: -2 + x = -2.236067978 Solving -2 + x = -2.236067978 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 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.236067978 + 2 x = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 x = -0.236067978 Simplifying x = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.236067978, -0.236067978}
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