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Simplifying 50x2 + -20x + 1 = 0 Reorder the terms: 1 + -20x + 50x2 = 0 Solving 1 + -20x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.02 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -0.4x + -0.02 + x2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + -0.4x + x2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -0.4x + x2 = 0 + -0.02 -0.4x + x2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 -0.4x + x2 = -0.02 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.02 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.02 + 0.04 Combine like terms: -0.02 + 0.04 = 0.02 0.04 + -0.4x + x2 = 0.02 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.02 Calculate the square root of the right side: 0.141421356 Break this problem into two subproblems by setting (x + -0.2) equal to 0.141421356 and -0.141421356.Subproblem 1
x + -0.2 = 0.141421356 Simplifying x + -0.2 = 0.141421356 Reorder the terms: -0.2 + x = 0.141421356 Solving -0.2 + x = 0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.141421356 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.141421356 + 0.2 x = 0.141421356 + 0.2 Combine like terms: 0.141421356 + 0.2 = 0.341421356 x = 0.341421356 Simplifying x = 0.341421356Subproblem 2
x + -0.2 = -0.141421356 Simplifying x + -0.2 = -0.141421356 Reorder the terms: -0.2 + x = -0.141421356 Solving -0.2 + x = -0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.141421356 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.141421356 + 0.2 x = -0.141421356 + 0.2 Combine like terms: -0.141421356 + 0.2 = 0.058578644 x = 0.058578644 Simplifying x = 0.058578644Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.341421356, 0.058578644}
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