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Simplifying 0.4x2 + -20x = -218 Reorder the terms: -20x + 0.4x2 = -218 Solving -20x + 0.4x2 = -218 Solving for variable 'x'. Reorder the terms: 218 + -20x + 0.4x2 = -218 + 218 Combine like terms: -218 + 218 = 0 218 + -20x + 0.4x2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 545 + -50x + x2 = 0 Move the constant term to the right: Add '-545' to each side of the equation. 545 + -50x + -545 + x2 = 0 + -545 Reorder the terms: 545 + -545 + -50x + x2 = 0 + -545 Combine like terms: 545 + -545 = 0 0 + -50x + x2 = 0 + -545 -50x + x2 = 0 + -545 Combine like terms: 0 + -545 = -545 -50x + x2 = -545 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -545 + 625 Reorder the terms: 625 + -50x + x2 = -545 + 625 Combine like terms: -545 + 625 = 80 625 + -50x + x2 = 80 Factor a perfect square on the left side: (x + -25)(x + -25) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -25) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -25 = 8.94427191 Simplifying x + -25 = 8.94427191 Reorder the terms: -25 + x = 8.94427191 Solving -25 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 8.94427191 + 25 Combine like terms: -25 + 25 = 0 0 + x = 8.94427191 + 25 x = 8.94427191 + 25 Combine like terms: 8.94427191 + 25 = 33.94427191 x = 33.94427191 Simplifying x = 33.94427191Subproblem 2
x + -25 = -8.94427191 Simplifying x + -25 = -8.94427191 Reorder the terms: -25 + x = -8.94427191 Solving -25 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -8.94427191 + 25 Combine like terms: -25 + 25 = 0 0 + x = -8.94427191 + 25 x = -8.94427191 + 25 Combine like terms: -8.94427191 + 25 = 16.05572809 x = 16.05572809 Simplifying x = 16.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.94427191, 16.05572809}
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