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Simplifying 2x2 + 1x = 38 Reorder the terms: 1x + 2x2 = 38 Solving 1x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + 1x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + 0.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 0.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 0.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 0.5x + x2 = 0 + 19 0.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 0.5x + x2 = 19 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 = 19 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 19 + 0.0625 Combine like terms: 19 + 0.0625 = 19.0625 0.0625 + 0.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + 0.25) equal to 4.366062299 and -4.366062299.Subproblem 1
x + 0.25 = 4.366062299 Simplifying x + 0.25 = 4.366062299 Reorder the terms: 0.25 + x = 4.366062299 Solving 0.25 + x = 4.366062299 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 = 4.366062299 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.366062299 + -0.25 x = 4.366062299 + -0.25 Combine like terms: 4.366062299 + -0.25 = 4.116062299 x = 4.116062299 Simplifying x = 4.116062299Subproblem 2
x + 0.25 = -4.366062299 Simplifying x + 0.25 = -4.366062299 Reorder the terms: 0.25 + x = -4.366062299 Solving 0.25 + x = -4.366062299 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 = -4.366062299 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.366062299 + -0.25 x = -4.366062299 + -0.25 Combine like terms: -4.366062299 + -0.25 = -4.616062299 x = -4.616062299 Simplifying x = -4.616062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.116062299, -4.616062299}
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