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Simplifying 2x2 + 0.15x + -0.045 = 0 Reorder the terms: -0.045 + 0.15x + 2x2 = 0 Solving -0.045 + 0.15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.0225 + 0.075x + x2 = 0 Move the constant term to the right: Add '0.0225' to each side of the equation. -0.0225 + 0.075x + 0.0225 + x2 = 0 + 0.0225 Reorder the terms: -0.0225 + 0.0225 + 0.075x + x2 = 0 + 0.0225 Combine like terms: -0.0225 + 0.0225 = 0.0000 0.0000 + 0.075x + x2 = 0 + 0.0225 0.075x + x2 = 0 + 0.0225 Combine like terms: 0 + 0.0225 = 0.0225 0.075x + x2 = 0.0225 The x term is 0.075x. Take half its coefficient (0.0375). Square it (0.00140625) and add it to both sides. Add '0.00140625' to each side of the equation. 0.075x + 0.00140625 + x2 = 0.0225 + 0.00140625 Reorder the terms: 0.00140625 + 0.075x + x2 = 0.0225 + 0.00140625 Combine like terms: 0.0225 + 0.00140625 = 0.02390625 0.00140625 + 0.075x + x2 = 0.02390625 Factor a perfect square on the left side: (x + 0.0375)(x + 0.0375) = 0.02390625 Calculate the square root of the right side: 0.154616461 Break this problem into two subproblems by setting (x + 0.0375) equal to 0.154616461 and -0.154616461.Subproblem 1
x + 0.0375 = 0.154616461 Simplifying x + 0.0375 = 0.154616461 Reorder the terms: 0.0375 + x = 0.154616461 Solving 0.0375 + x = 0.154616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0375' to each side of the equation. 0.0375 + -0.0375 + x = 0.154616461 + -0.0375 Combine like terms: 0.0375 + -0.0375 = 0.0000 0.0000 + x = 0.154616461 + -0.0375 x = 0.154616461 + -0.0375 Combine like terms: 0.154616461 + -0.0375 = 0.117116461 x = 0.117116461 Simplifying x = 0.117116461Subproblem 2
x + 0.0375 = -0.154616461 Simplifying x + 0.0375 = -0.154616461 Reorder the terms: 0.0375 + x = -0.154616461 Solving 0.0375 + x = -0.154616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0375' to each side of the equation. 0.0375 + -0.0375 + x = -0.154616461 + -0.0375 Combine like terms: 0.0375 + -0.0375 = 0.0000 0.0000 + x = -0.154616461 + -0.0375 x = -0.154616461 + -0.0375 Combine like terms: -0.154616461 + -0.0375 = -0.192116461 x = -0.192116461 Simplifying x = -0.192116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117116461, -0.192116461}
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