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Simplifying 5x2 + -2x + 0.05 = 0 Reorder the terms: 0.05 + -2x + 5x2 = 0 Solving 0.05 + -2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.01 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + -0.4x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + -0.4x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + -0.4x + x2 = 0 + -0.01 -0.4x + x2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 -0.4x + x2 = -0.01 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 = -0.01 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.01 + 0.04 Combine like terms: -0.01 + 0.04 = 0.03 0.04 + -0.4x + x2 = 0.03 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.03 Calculate the square root of the right side: 0.173205081 Break this problem into two subproblems by setting (x + -0.2) equal to 0.173205081 and -0.173205081.Subproblem 1
x + -0.2 = 0.173205081 Simplifying x + -0.2 = 0.173205081 Reorder the terms: -0.2 + x = 0.173205081 Solving -0.2 + x = 0.173205081 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 = 0.173205081 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.173205081 + 0.2 x = 0.173205081 + 0.2 Combine like terms: 0.173205081 + 0.2 = 0.373205081 x = 0.373205081 Simplifying x = 0.373205081Subproblem 2
x + -0.2 = -0.173205081 Simplifying x + -0.2 = -0.173205081 Reorder the terms: -0.2 + x = -0.173205081 Solving -0.2 + x = -0.173205081 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 = -0.173205081 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.173205081 + 0.2 x = -0.173205081 + 0.2 Combine like terms: -0.173205081 + 0.2 = 0.026794919 x = 0.026794919 Simplifying x = 0.026794919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.373205081, 0.026794919}
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