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Simplifying 4x2 + 3x + -1800 = 0 Reorder the terms: -1800 + 3x + 4x2 = 0 Solving -1800 + 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'. -450 + 0.75x + x2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + 0.75x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 0.75x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 0.75x + x2 = 0 + 450 0.75x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 0.75x + x2 = 450 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 = 450 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 450 + 0.140625 Combine like terms: 450 + 0.140625 = 450.140625 0.140625 + 0.75x + x2 = 450.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 450.140625 Calculate the square root of the right side: 21.21651774 Break this problem into two subproblems by setting (x + 0.375) equal to 21.21651774 and -21.21651774.Subproblem 1
x + 0.375 = 21.21651774 Simplifying x + 0.375 = 21.21651774 Reorder the terms: 0.375 + x = 21.21651774 Solving 0.375 + x = 21.21651774 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 = 21.21651774 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 21.21651774 + -0.375 x = 21.21651774 + -0.375 Combine like terms: 21.21651774 + -0.375 = 20.84151774 x = 20.84151774 Simplifying x = 20.84151774Subproblem 2
x + 0.375 = -21.21651774 Simplifying x + 0.375 = -21.21651774 Reorder the terms: 0.375 + x = -21.21651774 Solving 0.375 + x = -21.21651774 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 = -21.21651774 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -21.21651774 + -0.375 x = -21.21651774 + -0.375 Combine like terms: -21.21651774 + -0.375 = -21.59151774 x = -21.59151774 Simplifying x = -21.59151774Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.84151774, -21.59151774}
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