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Simplifying 4x2 + 17x + -22 = 0 Reorder the terms: -22 + 17x + 4x2 = 0 Solving -22 + 17x + 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'. -5.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4.25x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4.25x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4.25x + x2 = 0 + 5.5 4.25x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4.25x + x2 = 5.5 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 5.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 5.5 + 4.515625 Combine like terms: 5.5 + 4.515625 = 10.015625 4.515625 + 4.25x + x2 = 10.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 10.015625 Calculate the square root of the right side: 3.164747225 Break this problem into two subproblems by setting (x + 2.125) equal to 3.164747225 and -3.164747225.Subproblem 1
x + 2.125 = 3.164747225 Simplifying x + 2.125 = 3.164747225 Reorder the terms: 2.125 + x = 3.164747225 Solving 2.125 + x = 3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.164747225 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.164747225 + -2.125 x = 3.164747225 + -2.125 Combine like terms: 3.164747225 + -2.125 = 1.039747225 x = 1.039747225 Simplifying x = 1.039747225Subproblem 2
x + 2.125 = -3.164747225 Simplifying x + 2.125 = -3.164747225 Reorder the terms: 2.125 + x = -3.164747225 Solving 2.125 + x = -3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.164747225 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.164747225 + -2.125 x = -3.164747225 + -2.125 Combine like terms: -3.164747225 + -2.125 = -5.289747225 x = -5.289747225 Simplifying x = -5.289747225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.039747225, -5.289747225}
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