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Simplifying 4x2 + 3x + -75 = 0 Reorder the terms: -75 + 3x + 4x2 = 0 Solving -75 + 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'. -18.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 0.75x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 0.75x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 0.75x + x2 = 0 + 18.75 0.75x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 0.75x + x2 = 18.75 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 = 18.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 18.75 + 0.140625 Combine like terms: 18.75 + 0.140625 = 18.890625 0.140625 + 0.75x + x2 = 18.890625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 18.890625 Calculate the square root of the right side: 4.346334663 Break this problem into two subproblems by setting (x + 0.375) equal to 4.346334663 and -4.346334663.Subproblem 1
x + 0.375 = 4.346334663 Simplifying x + 0.375 = 4.346334663 Reorder the terms: 0.375 + x = 4.346334663 Solving 0.375 + x = 4.346334663 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 = 4.346334663 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 4.346334663 + -0.375 x = 4.346334663 + -0.375 Combine like terms: 4.346334663 + -0.375 = 3.971334663 x = 3.971334663 Simplifying x = 3.971334663Subproblem 2
x + 0.375 = -4.346334663 Simplifying x + 0.375 = -4.346334663 Reorder the terms: 0.375 + x = -4.346334663 Solving 0.375 + x = -4.346334663 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 = -4.346334663 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -4.346334663 + -0.375 x = -4.346334663 + -0.375 Combine like terms: -4.346334663 + -0.375 = -4.721334663 x = -4.721334663 Simplifying x = -4.721334663Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.971334663, -4.721334663}
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