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Simplifying 4x2 + 21x + 22 = -4x + 4 Reorder the terms: 22 + 21x + 4x2 = -4x + 4 Reorder the terms: 22 + 21x + 4x2 = 4 + -4x Solving 22 + 21x + 4x2 = 4 + -4x Solving for variable 'x'. Reorder the terms: 22 + -4 + 21x + 4x + 4x2 = 4 + -4x + -4 + 4x Combine like terms: 22 + -4 = 18 18 + 21x + 4x + 4x2 = 4 + -4x + -4 + 4x Combine like terms: 21x + 4x = 25x 18 + 25x + 4x2 = 4 + -4x + -4 + 4x Reorder the terms: 18 + 25x + 4x2 = 4 + -4 + -4x + 4x Combine like terms: 4 + -4 = 0 18 + 25x + 4x2 = 0 + -4x + 4x 18 + 25x + 4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 18 + 25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + 6.25x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 6.25x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 6.25x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 6.25x + x2 = 0 + -4.5 6.25x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 6.25x + x2 = -4.5 The x term is 6.25x. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25x + 9.765625 + x2 = -4.5 + 9.765625 Reorder the terms: 9.765625 + 6.25x + x2 = -4.5 + 9.765625 Combine like terms: -4.5 + 9.765625 = 5.265625 9.765625 + 6.25x + x2 = 5.265625 Factor a perfect square on the left side: (x + 3.125)(x + 3.125) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + 3.125) equal to 2.294694969 and -2.294694969.Subproblem 1
x + 3.125 = 2.294694969 Simplifying x + 3.125 = 2.294694969 Reorder the terms: 3.125 + x = 2.294694969 Solving 3.125 + x = 2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 2.294694969 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 2.294694969 + -3.125 x = 2.294694969 + -3.125 Combine like terms: 2.294694969 + -3.125 = -0.830305031 x = -0.830305031 Simplifying x = -0.830305031Subproblem 2
x + 3.125 = -2.294694969 Simplifying x + 3.125 = -2.294694969 Reorder the terms: 3.125 + x = -2.294694969 Solving 3.125 + x = -2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -2.294694969 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -2.294694969 + -3.125 x = -2.294694969 + -3.125 Combine like terms: -2.294694969 + -3.125 = -5.419694969 x = -5.419694969 Simplifying x = -5.419694969Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.830305031, -5.419694969}
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