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Simplifying 0.25x2 + -1x + 0.8 = 0 Reorder the terms: 0.8 + -1x + 0.25x2 = 0 Solving 0.8 + -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'. 3.2 + -4x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -4x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -4x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -4x + x2 = 0 + -3.2 -4x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -4x + x2 = -3.2 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 = -3.2 + 4 Reorder the terms: 4 + -4x + x2 = -3.2 + 4 Combine like terms: -3.2 + 4 = 0.8 4 + -4x + x2 = 0.8 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + -2) equal to 0.894427191 and -0.894427191.Subproblem 1
x + -2 = 0.894427191 Simplifying x + -2 = 0.894427191 Reorder the terms: -2 + x = 0.894427191 Solving -2 + x = 0.894427191 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 = 0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.894427191 + 2 x = 0.894427191 + 2 Combine like terms: 0.894427191 + 2 = 2.894427191 x = 2.894427191 Simplifying x = 2.894427191Subproblem 2
x + -2 = -0.894427191 Simplifying x + -2 = -0.894427191 Reorder the terms: -2 + x = -0.894427191 Solving -2 + x = -0.894427191 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 = -0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.894427191 + 2 x = -0.894427191 + 2 Combine like terms: -0.894427191 + 2 = 1.105572809 x = 1.105572809 Simplifying x = 1.105572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.894427191, 1.105572809}
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