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Simplifying -0.2x2 + 0.4x + 0.8 = 0 Reorder the terms: 0.8 + 0.4x + -0.2x2 = 0 Solving 0.8 + 0.4x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -4 + -2x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2x + x2 = 0 + 4 -2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2x + x2 = 4 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 = 4 + 1 Reorder the terms: 1 + -2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2x + x2 = 5 Factor a perfect square on the left side: (x + -1)(x + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -1 = 2.236067978 Simplifying x + -1 = 2.236067978 Reorder the terms: -1 + x = 2.236067978 Solving -1 + x = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.236067978 + 1 x = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 x = 3.236067978 Simplifying x = 3.236067978Subproblem 2
x + -1 = -2.236067978 Simplifying x + -1 = -2.236067978 Reorder the terms: -1 + x = -2.236067978 Solving -1 + x = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.236067978 + 1 x = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 x = -1.236067978 Simplifying x = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236067978, -1.236067978}
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