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Simplifying x2 + -0.6x + 0.08 = 0 Reorder the terms: 0.08 + -0.6x + x2 = 0 Solving 0.08 + -0.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.6x + -0.08 + x2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.6x + x2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.6x + x2 = 0 + -0.08 -0.6x + x2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 -0.6x + x2 = -0.08 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -0.08 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -0.08 + 0.09 Combine like terms: -0.08 + 0.09 = 0.01 0.09 + -0.6x + x2 = 0.01 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (x + -0.3) equal to 0.1 and -0.1.Subproblem 1
x + -0.3 = 0.1 Simplifying x + -0.3 = 0.1 Reorder the terms: -0.3 + x = 0.1 Solving -0.3 + x = 0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.1 + 0.3 x = 0.1 + 0.3 Combine like terms: 0.1 + 0.3 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.3 = -0.1 Simplifying x + -0.3 = -0.1 Reorder the terms: -0.3 + x = -0.1 Solving -0.3 + x = -0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.1 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.1 + 0.3 x = -0.1 + 0.3 Combine like terms: -0.1 + 0.3 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, 0.2}
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