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Simplifying x2 + 0.3x + -0.1 = 0 Reorder the terms: -0.1 + 0.3x + x2 = 0 Solving -0.1 + 0.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.3x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.3x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.3x + x2 = 0 + 0.1 0.3x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.3x + x2 = 0.1 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 = 0.1 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.1 + 0.0225 Combine like terms: 0.1 + 0.0225 = 0.1225 0.0225 + 0.3x + x2 = 0.1225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.1225 Calculate the square root of the right side: 0.35 Break this problem into two subproblems by setting (x + 0.15) equal to 0.35 and -0.35.Subproblem 1
x + 0.15 = 0.35 Simplifying x + 0.15 = 0.35 Reorder the terms: 0.15 + x = 0.35 Solving 0.15 + x = 0.35 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 = 0.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.35 + -0.15 x = 0.35 + -0.15 Combine like terms: 0.35 + -0.15 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + 0.15 = -0.35 Simplifying x + 0.15 = -0.35 Reorder the terms: 0.15 + x = -0.35 Solving 0.15 + x = -0.35 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 = -0.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.35 + -0.15 x = -0.35 + -0.15 Combine like terms: -0.35 + -0.15 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, -0.5}
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