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Simplifying -0.25x2 + -1x + -1 = 0 Reorder the terms: -1 + -1x + -0.25x2 = 0 Solving -1 + -1x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. 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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