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Simplifying 4x2 + 76x + 93 = 0 Reorder the terms: 93 + 76x + 4x2 = 0 Solving 93 + 76x + 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'. 23.25 + 19x + x2 = 0 Move the constant term to the right: Add '-23.25' to each side of the equation. 23.25 + 19x + -23.25 + x2 = 0 + -23.25 Reorder the terms: 23.25 + -23.25 + 19x + x2 = 0 + -23.25 Combine like terms: 23.25 + -23.25 = 0.00 0.00 + 19x + x2 = 0 + -23.25 19x + x2 = 0 + -23.25 Combine like terms: 0 + -23.25 = -23.25 19x + x2 = -23.25 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -23.25 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -23.25 + 90.25 Combine like terms: -23.25 + 90.25 = 67 90.25 + 19x + x2 = 67 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 9.5) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 9.5 = 8.185352772 Simplifying x + 9.5 = 8.185352772 Reorder the terms: 9.5 + x = 8.185352772 Solving 9.5 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 8.185352772 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.185352772 + -9.5 x = 8.185352772 + -9.5 Combine like terms: 8.185352772 + -9.5 = -1.314647228 x = -1.314647228 Simplifying x = -1.314647228Subproblem 2
x + 9.5 = -8.185352772 Simplifying x + 9.5 = -8.185352772 Reorder the terms: 9.5 + x = -8.185352772 Solving 9.5 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -8.185352772 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.185352772 + -9.5 x = -8.185352772 + -9.5 Combine like terms: -8.185352772 + -9.5 = -17.685352772 x = -17.685352772 Simplifying x = -17.685352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.314647228, -17.685352772}
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