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Simplifying 2x2 + 1x = 8 Reorder the terms: 1x + 2x2 = 8 Solving 1x + 2x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 1x + 2x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 0.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.5x + x2 = 0 + 4 0.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.5x + x2 = 4 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 = 4 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + 0.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 0.25 = 2.015564437 Simplifying x + 0.25 = 2.015564437 Reorder the terms: 0.25 + x = 2.015564437 Solving 0.25 + x = 2.015564437 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 = 2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.015564437 + -0.25 x = 2.015564437 + -0.25 Combine like terms: 2.015564437 + -0.25 = 1.765564437 x = 1.765564437 Simplifying x = 1.765564437Subproblem 2
x + 0.25 = -2.015564437 Simplifying x + 0.25 = -2.015564437 Reorder the terms: 0.25 + x = -2.015564437 Solving 0.25 + x = -2.015564437 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 = -2.015564437 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.015564437 + -0.25 x = -2.015564437 + -0.25 Combine like terms: -2.015564437 + -0.25 = -2.265564437 x = -2.265564437 Simplifying x = -2.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.765564437, -2.265564437}
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