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Simplifying 0.25x2 + -5x + 5 = 0 Reorder the terms: 5 + -5x + 0.25x2 = 0 Solving 5 + -5x + 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'. 20 + -20x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -20x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -20x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -20x + x2 = 0 + -20 -20x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -20x + x2 = -20 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -20 + 100 Reorder the terms: 100 + -20x + x2 = -20 + 100 Combine like terms: -20 + 100 = 80 100 + -20x + x2 = 80 Factor a perfect square on the left side: (x + -10)(x + -10) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -10) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -10 = 8.94427191 Simplifying x + -10 = 8.94427191 Reorder the terms: -10 + x = 8.94427191 Solving -10 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.94427191 + 10 x = 8.94427191 + 10 Combine like terms: 8.94427191 + 10 = 18.94427191 x = 18.94427191 Simplifying x = 18.94427191Subproblem 2
x + -10 = -8.94427191 Simplifying x + -10 = -8.94427191 Reorder the terms: -10 + x = -8.94427191 Solving -10 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -8.94427191 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.94427191 + 10 x = -8.94427191 + 10 Combine like terms: -8.94427191 + 10 = 1.05572809 x = 1.05572809 Simplifying x = 1.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.94427191, 1.05572809}
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