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Simplifying 0.8x + -0.2x2 + 1 = 0 Reorder the terms: 1 + 0.8x + -0.2x2 = 0 Solving 1 + 0.8x + -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'. -5 + -4x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x + x2 = 0 + 5 -4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4x + x2 = 5 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 = 5 + 4 Reorder the terms: 4 + -4x + x2 = 5 + 4 Combine like terms: 5 + 4 = 9 4 + -4x + x2 = 9 Factor a perfect square on the left side: (x + -2)(x + -2) = 9 Calculate the square root of the right side: 3 Break this problem into two subproblems by setting (x + -2) equal to 3 and -3.Subproblem 1
x + -2 = 3 Simplifying x + -2 = 3 Reorder the terms: -2 + x = 3 Solving -2 + x = 3 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 = 3 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3 + 2 x = 3 + 2 Combine like terms: 3 + 2 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -2 = -3 Simplifying x + -2 = -3 Reorder the terms: -2 + x = -3 Solving -2 + x = -3 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 = -3 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3 + 2 x = -3 + 2 Combine like terms: -3 + 2 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -1}
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