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Simplifying 2x2 + 1.5x + 0.28 = 0 Reorder the terms: 0.28 + 1.5x + 2x2 = 0 Solving 0.28 + 1.5x + 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'. 0.14 + 0.75x + x2 = 0 Move the constant term to the right: Add '-0.14' to each side of the equation. 0.14 + 0.75x + -0.14 + x2 = 0 + -0.14 Reorder the terms: 0.14 + -0.14 + 0.75x + x2 = 0 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + 0.75x + x2 = 0 + -0.14 0.75x + x2 = 0 + -0.14 Combine like terms: 0 + -0.14 = -0.14 0.75x + x2 = -0.14 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -0.14 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -0.14 + 0.140625 Combine like terms: -0.14 + 0.140625 = 0.000625 0.140625 + 0.75x + x2 = 0.000625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.000625 Calculate the square root of the right side: 0.025 Break this problem into two subproblems by setting (x + 0.375) equal to 0.025 and -0.025.Subproblem 1
x + 0.375 = 0.025 Simplifying x + 0.375 = 0.025 Reorder the terms: 0.375 + x = 0.025 Solving 0.375 + x = 0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.025 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.025 + -0.375 x = 0.025 + -0.375 Combine like terms: 0.025 + -0.375 = -0.35 x = -0.35 Simplifying x = -0.35Subproblem 2
x + 0.375 = -0.025 Simplifying x + 0.375 = -0.025 Reorder the terms: 0.375 + x = -0.025 Solving 0.375 + x = -0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.025 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.025 + -0.375 x = -0.025 + -0.375 Combine like terms: -0.025 + -0.375 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.35, -0.4}
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