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Simplifying x2 + -0.54x + 0.02 = 0 Reorder the terms: 0.02 + -0.54x + x2 = 0 Solving 0.02 + -0.54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.02' to each side of the equation. 0.02 + -0.54x + -0.02 + x2 = 0 + -0.02 Reorder the terms: 0.02 + -0.02 + -0.54x + x2 = 0 + -0.02 Combine like terms: 0.02 + -0.02 = 0.00 0.00 + -0.54x + x2 = 0 + -0.02 -0.54x + x2 = 0 + -0.02 Combine like terms: 0 + -0.02 = -0.02 -0.54x + x2 = -0.02 The x term is -0.54x. Take half its coefficient (-0.27). Square it (0.0729) and add it to both sides. Add '0.0729' to each side of the equation. -0.54x + 0.0729 + x2 = -0.02 + 0.0729 Reorder the terms: 0.0729 + -0.54x + x2 = -0.02 + 0.0729 Combine like terms: -0.02 + 0.0729 = 0.0529 0.0729 + -0.54x + x2 = 0.0529 Factor a perfect square on the left side: (x + -0.27)(x + -0.27) = 0.0529 Calculate the square root of the right side: 0.23 Break this problem into two subproblems by setting (x + -0.27) equal to 0.23 and -0.23.Subproblem 1
x + -0.27 = 0.23 Simplifying x + -0.27 = 0.23 Reorder the terms: -0.27 + x = 0.23 Solving -0.27 + x = 0.23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.27' to each side of the equation. -0.27 + 0.27 + x = 0.23 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + x = 0.23 + 0.27 x = 0.23 + 0.27 Combine like terms: 0.23 + 0.27 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + -0.27 = -0.23 Simplifying x + -0.27 = -0.23 Reorder the terms: -0.27 + x = -0.23 Solving -0.27 + x = -0.23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.27' to each side of the equation. -0.27 + 0.27 + x = -0.23 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + x = -0.23 + 0.27 x = -0.23 + 0.27 Combine like terms: -0.23 + 0.27 = 0.04 x = 0.04 Simplifying x = 0.04Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, 0.04}
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