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Simplifying 2x2 + -1x + -24 = 20 Reorder the terms: -24 + -1x + 2x2 = 20 Solving -24 + -1x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -24 + -20 + -1x + 2x2 = 20 + -20 Combine like terms: -24 + -20 = -44 -44 + -1x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -44 + -1x + 2x2 = 0 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 = 4.947073557 x = 4.947073557 Simplifying x = 4.947073557Subproblem 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 = -4.447073557 x = -4.447073557 Simplifying x = -4.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.947073557, -4.447073557}
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