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Simplifying 50 = 2x2 + x Reorder the terms: 50 = x + 2x2 Solving 50 = x + 2x2 Solving for variable 'x'. Reorder the terms: 50 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 50 + -1x + -2x2 = 0 + 2x2 + -2x2 50 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 50 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -25 + 0.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 0.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.5x + x2 = 0 + 25 0.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.5x + x2 = 25 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 = 25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 25 + 0.0625 Combine like terms: 25 + 0.0625 = 25.0625 0.0625 + 0.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + 0.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + 0.25 = 5.006246099 Simplifying x + 0.25 = 5.006246099 Reorder the terms: 0.25 + x = 5.006246099 Solving 0.25 + x = 5.006246099 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 = 5.006246099 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 5.006246099 + -0.25 x = 5.006246099 + -0.25 Combine like terms: 5.006246099 + -0.25 = 4.756246099 x = 4.756246099 Simplifying x = 4.756246099Subproblem 2
x + 0.25 = -5.006246099 Simplifying x + 0.25 = -5.006246099 Reorder the terms: 0.25 + x = -5.006246099 Solving 0.25 + x = -5.006246099 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 = -5.006246099 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -5.006246099 + -0.25 x = -5.006246099 + -0.25 Combine like terms: -5.006246099 + -0.25 = -5.256246099 x = -5.256246099 Simplifying x = -5.256246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.756246099, -5.256246099}
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