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Simplifying x2 + 0.3x + -0.02 = 0 Reorder the terms: -0.02 + 0.3x + x2 = 0 Solving -0.02 + 0.3x + 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 + 0.3x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + 0.3x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + 0.3x + x2 = 0 + 0.02 0.3x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 0.3x + x2 = 0.02 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.02 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.02 + 0.0225 Combine like terms: 0.02 + 0.0225 = 0.0425 0.0225 + 0.3x + x2 = 0.0425 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.0425 Calculate the square root of the right side: 0.206155281 Break this problem into two subproblems by setting (x + 0.15) equal to 0.206155281 and -0.206155281.Subproblem 1
x + 0.15 = 0.206155281 Simplifying x + 0.15 = 0.206155281 Reorder the terms: 0.15 + x = 0.206155281 Solving 0.15 + x = 0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.206155281 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.206155281 + -0.15 x = 0.206155281 + -0.15 Combine like terms: 0.206155281 + -0.15 = 0.056155281 x = 0.056155281 Simplifying x = 0.056155281Subproblem 2
x + 0.15 = -0.206155281 Simplifying x + 0.15 = -0.206155281 Reorder the terms: 0.15 + x = -0.206155281 Solving 0.15 + x = -0.206155281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.206155281 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.206155281 + -0.15 x = -0.206155281 + -0.15 Combine like terms: -0.206155281 + -0.15 = -0.356155281 x = -0.356155281 Simplifying x = -0.356155281Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.056155281, -0.356155281}
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