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Simplifying x2 + 0.08x + -0.08 = 0 Reorder the terms: -0.08 + 0.08x + x2 = 0 Solving -0.08 + 0.08x + 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 + 0.08x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.08x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.08x + x2 = 0 + 0.08 0.08x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.08x + x2 = 0.08 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = 0.08 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = 0.08 + 0.0016 Combine like terms: 0.08 + 0.0016 = 0.0816 0.0016 + 0.08x + x2 = 0.0816 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = 0.0816 Calculate the square root of the right side: 0.285657137 Break this problem into two subproblems by setting (x + 0.04) equal to 0.285657137 and -0.285657137.Subproblem 1
x + 0.04 = 0.285657137 Simplifying x + 0.04 = 0.285657137 Reorder the terms: 0.04 + x = 0.285657137 Solving 0.04 + x = 0.285657137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 0.285657137 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 0.285657137 + -0.04 x = 0.285657137 + -0.04 Combine like terms: 0.285657137 + -0.04 = 0.245657137 x = 0.245657137 Simplifying x = 0.245657137Subproblem 2
x + 0.04 = -0.285657137 Simplifying x + 0.04 = -0.285657137 Reorder the terms: 0.04 + x = -0.285657137 Solving 0.04 + x = -0.285657137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = -0.285657137 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = -0.285657137 + -0.04 x = -0.285657137 + -0.04 Combine like terms: -0.285657137 + -0.04 = -0.325657137 x = -0.325657137 Simplifying x = -0.325657137Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.245657137, -0.325657137}
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