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Simplifying x(2x + -1) = 212 Reorder the terms: x(-1 + 2x) = 212 (-1 * x + 2x * x) = 212 (-1x + 2x2) = 212 Solving -1x + 2x2 = 212 Solving for variable 'x'. Reorder the terms: -212 + -1x + 2x2 = 212 + -212 Combine like terms: 212 + -212 = 0 -212 + -1x + 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 -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 = 106 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 106 + 0.0625 Combine like terms: 106 + 0.0625 = 106.0625 0.0625 + -0.5x + x2 = 106.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 106.0625 Calculate the square root of the right side: 10.298664962 Break this problem into two subproblems by setting (x + -0.25) equal to 10.298664962 and -10.298664962.Subproblem 1
x + -0.25 = 10.298664962 Simplifying x + -0.25 = 10.298664962 Reorder the terms: -0.25 + x = 10.298664962 Solving -0.25 + x = 10.298664962 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 = 10.298664962 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 10.298664962 + 0.25 x = 10.298664962 + 0.25 Combine like terms: 10.298664962 + 0.25 = 10.548664962 x = 10.548664962 Simplifying x = 10.548664962Subproblem 2
x + -0.25 = -10.298664962 Simplifying x + -0.25 = -10.298664962 Reorder the terms: -0.25 + x = -10.298664962 Solving -0.25 + x = -10.298664962 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 = -10.298664962 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -10.298664962 + 0.25 x = -10.298664962 + 0.25 Combine like terms: -10.298664962 + 0.25 = -10.048664962 x = -10.048664962 Simplifying x = -10.048664962Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.548664962, -10.048664962}
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