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Simplifying 4X2 + 23X + 23 = 0 Reorder the terms: 23 + 23X + 4X2 = 0 Solving 23 + 23X + 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'. 5.75 + 5.75X + X2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + 5.75X + -5.75 + X2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + 5.75X + X2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + 5.75X + X2 = 0 + -5.75 5.75X + X2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 5.75X + X2 = -5.75 The X term is 5.75X. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75X + 8.265625 + X2 = -5.75 + 8.265625 Reorder the terms: 8.265625 + 5.75X + X2 = -5.75 + 8.265625 Combine like terms: -5.75 + 8.265625 = 2.515625 8.265625 + 5.75X + X2 = 2.515625 Factor a perfect square on the left side: (X + 2.875)(X + 2.875) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (X + 2.875) equal to 1.586072193 and -1.586072193.Subproblem 1
X + 2.875 = 1.586072193 Simplifying X + 2.875 = 1.586072193 Reorder the terms: 2.875 + X = 1.586072193 Solving 2.875 + X = 1.586072193 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + X = 1.586072193 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + X = 1.586072193 + -2.875 X = 1.586072193 + -2.875 Combine like terms: 1.586072193 + -2.875 = -1.288927807 X = -1.288927807 Simplifying X = -1.288927807Subproblem 2
X + 2.875 = -1.586072193 Simplifying X + 2.875 = -1.586072193 Reorder the terms: 2.875 + X = -1.586072193 Solving 2.875 + X = -1.586072193 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + X = -1.586072193 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + X = -1.586072193 + -2.875 X = -1.586072193 + -2.875 Combine like terms: -1.586072193 + -2.875 = -4.461072193 X = -4.461072193 Simplifying X = -4.461072193Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.288927807, -4.461072193}
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