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