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Simplifying 2x2 + 1x + -44 = 0 Reorder the terms: -44 + 1x + 2x2 = 0 Solving -44 + 1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22 + 0.5x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 0.5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 0.5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 0.5x + x2 = 0 + 22 0.5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 0.5x + x2 = 22 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 22 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 22 + 0.0625 Combine like terms: 22 + 0.0625 = 22.0625 0.0625 + 0.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 0.25) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 0.25 = 4.697073557 Simplifying x + 0.25 = 4.697073557 Reorder the terms: 0.25 + x = 4.697073557 Solving 0.25 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.697073557 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.697073557 + -0.25 x = 4.697073557 + -0.25 Combine like terms: 4.697073557 + -0.25 = 4.447073557 x = 4.447073557 Simplifying x = 4.447073557Subproblem 2
x + 0.25 = -4.697073557 Simplifying x + 0.25 = -4.697073557 Reorder the terms: 0.25 + x = -4.697073557 Solving 0.25 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.697073557 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.697073557 + -0.25 x = -4.697073557 + -0.25 Combine like terms: -4.697073557 + -0.25 = -4.947073557 x = -4.947073557 Simplifying x = -4.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.447073557, -4.947073557}
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