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Simplifying 2x2 + x = 212 Reorder the terms: x + 2x2 = 212 Solving x + 2x2 = 212 Solving for variable 'x'. Reorder the terms: -212 + x + 2x2 = 212 + -212 Combine like terms: 212 + -212 = 0 -212 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -106 + 0.5x + x2 = 0 Move the constant term to the right: Add '106' to each side of the equation. -106 + 0.5x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 0.5x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 0.5x + x2 = 0 + 106 0.5x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 0.5x + x2 = 106 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 = 106 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 106 + 0.25 Combine like terms: 106 + 0.25 = 106.25 0.25 + 0.5x + x2 = 106.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + 0.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + 0.5 = 10.307764064 Simplifying x + 0.5 = 10.307764064 Reorder the terms: 0.5 + x = 10.307764064 Solving 0.5 + x = 10.307764064 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 = 10.307764064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.307764064 + -0.5 x = 10.307764064 + -0.5 Combine like terms: 10.307764064 + -0.5 = 9.807764064 x = 9.807764064 Simplifying x = 9.807764064Subproblem 2
x + 0.5 = -10.307764064 Simplifying x + 0.5 = -10.307764064 Reorder the terms: 0.5 + x = -10.307764064 Solving 0.5 + x = -10.307764064 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 = -10.307764064 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.307764064 + -0.5 x = -10.307764064 + -0.5 Combine like terms: -10.307764064 + -0.5 = -10.807764064 x = -10.807764064 Simplifying x = -10.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.807764064, -10.807764064}
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