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Simplifying 2x2 + 3x + 1 = 44 Reorder the terms: 1 + 3x + 2x2 = 44 Solving 1 + 3x + 2x2 = 44 Solving for variable 'x'. Reorder the terms: 1 + -44 + 3x + 2x2 = 44 + -44 Combine like terms: 1 + -44 = -43 -43 + 3x + 2x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -43 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + 1.5x + 21.5 + x2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + 1.5x + x2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + 1.5x + x2 = 0 + 21.5 1.5x + x2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 1.5x + x2 = 21.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 21.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 21.5 + 0.5625 Combine like terms: 21.5 + 0.5625 = 22.0625 0.5625 + 1.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 0.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 0.75 = 4.697073557 Simplifying x + 0.75 = 4.697073557 Reorder the terms: 0.75 + x = 4.697073557 Solving 0.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.697073557 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.697073557 + -0.75 x = 4.697073557 + -0.75 Combine like terms: 4.697073557 + -0.75 = 3.947073557 x = 3.947073557 Simplifying x = 3.947073557Subproblem 2
x + 0.75 = -4.697073557 Simplifying x + 0.75 = -4.697073557 Reorder the terms: 0.75 + x = -4.697073557 Solving 0.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.697073557 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.697073557 + -0.75 x = -4.697073557 + -0.75 Combine like terms: -4.697073557 + -0.75 = -5.447073557 x = -5.447073557 Simplifying x = -5.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.947073557, -5.447073557}
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