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Simplifying 22x + 2x2 + 3 = x Reorder the terms: 3 + 22x + 2x2 = x Solving 3 + 22x + 2x2 = x Solving for variable 'x'. Reorder the terms: 3 + 22x + -1x + 2x2 = x + -1x Combine like terms: 22x + -1x = 21x 3 + 21x + 2x2 = x + -1x Combine like terms: x + -1x = 0 3 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 10.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 10.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 10.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 10.5x + x2 = 0 + -1.5 10.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 10.5x + x2 = -1.5 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = -1.5 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -1.5 + 27.5625 Combine like terms: -1.5 + 27.5625 = 26.0625 27.5625 + 10.5x + x2 = 26.0625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (x + 5.25) equal to 5.105144464 and -5.105144464.Subproblem 1
x + 5.25 = 5.105144464 Simplifying x + 5.25 = 5.105144464 Reorder the terms: 5.25 + x = 5.105144464 Solving 5.25 + x = 5.105144464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 5.105144464 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 5.105144464 + -5.25 x = 5.105144464 + -5.25 Combine like terms: 5.105144464 + -5.25 = -0.144855536 x = -0.144855536 Simplifying x = -0.144855536Subproblem 2
x + 5.25 = -5.105144464 Simplifying x + 5.25 = -5.105144464 Reorder the terms: 5.25 + x = -5.105144464 Solving 5.25 + x = -5.105144464 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -5.105144464 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -5.105144464 + -5.25 x = -5.105144464 + -5.25 Combine like terms: -5.105144464 + -5.25 = -10.355144464 x = -10.355144464 Simplifying x = -10.355144464Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.144855536, -10.355144464}
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