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Simplifying 4x2 + 3x + -1.44 = 0 Reorder the terms: -1.44 + 3x + 4x2 = 0 Solving -1.44 + 3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.36 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.75x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.75x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.75x + x2 = 0 + 0.36 0.75x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.75x + x2 = 0.36 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 = 0.36 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.36 + 0.140625 Combine like terms: 0.36 + 0.140625 = 0.500625 0.140625 + 0.75x + x2 = 0.500625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.500625 Calculate the square root of the right side: 0.707548585 Break this problem into two subproblems by setting (x + 0.375) equal to 0.707548585 and -0.707548585.Subproblem 1
x + 0.375 = 0.707548585 Simplifying x + 0.375 = 0.707548585 Reorder the terms: 0.375 + x = 0.707548585 Solving 0.375 + x = 0.707548585 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 = 0.707548585 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.707548585 + -0.375 x = 0.707548585 + -0.375 Combine like terms: 0.707548585 + -0.375 = 0.332548585 x = 0.332548585 Simplifying x = 0.332548585Subproblem 2
x + 0.375 = -0.707548585 Simplifying x + 0.375 = -0.707548585 Reorder the terms: 0.375 + x = -0.707548585 Solving 0.375 + x = -0.707548585 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 = -0.707548585 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.707548585 + -0.375 x = -0.707548585 + -0.375 Combine like terms: -0.707548585 + -0.375 = -1.082548585 x = -1.082548585 Simplifying x = -1.082548585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.332548585, -1.082548585}
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