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Simplifying 2x2 + x = 38 Reorder the terms: x + 2x2 = 38 Solving x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + x + 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 x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 19 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 19 + 0.25 Combine like terms: 19 + 0.25 = 19.25 0.25 + 0.5x + x2 = 19.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 0.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 0.5 = 4.387482194 Simplifying x + 0.5 = 4.387482194 Reorder the terms: 0.5 + x = 4.387482194 Solving 0.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.387482194 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.387482194 + -0.5 x = 4.387482194 + -0.5 Combine like terms: 4.387482194 + -0.5 = 3.887482194 x = 3.887482194 Simplifying x = 3.887482194Subproblem 2
x + 0.5 = -4.387482194 Simplifying x + 0.5 = -4.387482194 Reorder the terms: 0.5 + x = -4.387482194 Solving 0.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.387482194 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.387482194 + -0.5 x = -4.387482194 + -0.5 Combine like terms: -4.387482194 + -0.5 = -4.887482194 x = -4.887482194 Simplifying x = -4.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.887482194, -4.887482194}
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