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Simplifying 4x2 + -19x + 24 = 4x + 1 Reorder the terms: 24 + -19x + 4x2 = 4x + 1 Reorder the terms: 24 + -19x + 4x2 = 1 + 4x Solving 24 + -19x + 4x2 = 1 + 4x Solving for variable 'x'. Reorder the terms: 24 + -1 + -19x + -4x + 4x2 = 1 + 4x + -1 + -4x Combine like terms: 24 + -1 = 23 23 + -19x + -4x + 4x2 = 1 + 4x + -1 + -4x Combine like terms: -19x + -4x = -23x 23 + -23x + 4x2 = 1 + 4x + -1 + -4x Reorder the terms: 23 + -23x + 4x2 = 1 + -1 + 4x + -4x Combine like terms: 1 + -1 = 0 23 + -23x + 4x2 = 0 + 4x + -4x 23 + -23x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 23 + -23x + 4x2 = 0 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 = 4.461072193 x = 4.461072193 Simplifying x = 4.461072193Subproblem 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 = 1.288927807 x = 1.288927807 Simplifying x = 1.288927807Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.461072193, 1.288927807}
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