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Simplifying 4x2 + -23x + 17 = -3 + 8 Reorder the terms: 17 + -23x + 4x2 = -3 + 8 Combine like terms: -3 + 8 = 5 17 + -23x + 4x2 = 5 Solving 17 + -23x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: 17 + -5 + -23x + 4x2 = 5 + -5 Combine like terms: 17 + -5 = 12 12 + -23x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 12 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + -5.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.75x + x2 = 0 + -3 -5.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.75x + x2 = -3 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 = -3 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -3 + 8.265625 Combine like terms: -3 + 8.265625 = 5.265625 8.265625 + -5.75x + x2 = 5.265625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + -2.875) equal to 2.294694969 and -2.294694969.Subproblem 1
x + -2.875 = 2.294694969 Simplifying x + -2.875 = 2.294694969 Reorder the terms: -2.875 + x = 2.294694969 Solving -2.875 + x = 2.294694969 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 = 2.294694969 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.294694969 + 2.875 x = 2.294694969 + 2.875 Combine like terms: 2.294694969 + 2.875 = 5.169694969 x = 5.169694969 Simplifying x = 5.169694969Subproblem 2
x + -2.875 = -2.294694969 Simplifying x + -2.875 = -2.294694969 Reorder the terms: -2.875 + x = -2.294694969 Solving -2.875 + x = -2.294694969 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 = -2.294694969 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.294694969 + 2.875 x = -2.294694969 + 2.875 Combine like terms: -2.294694969 + 2.875 = 0.580305031 x = 0.580305031 Simplifying x = 0.580305031Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.169694969, 0.580305031}
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