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Simplifying 2x2 + -21x = 1 Reorder the terms: -21x + 2x2 = 1 Solving -21x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -21x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -10.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -10.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -10.5x + x2 = 0 + 0.5 -10.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -10.5x + x2 = 0.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 0.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 0.5 + 27.5625 Combine like terms: 0.5 + 27.5625 = 28.0625 27.5625 + -10.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + -5.25) equal to 5.297405025 and -5.297405025.Subproblem 1
x + -5.25 = 5.297405025 Simplifying x + -5.25 = 5.297405025 Reorder the terms: -5.25 + x = 5.297405025 Solving -5.25 + x = 5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 5.297405025 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 5.297405025 + 5.25 x = 5.297405025 + 5.25 Combine like terms: 5.297405025 + 5.25 = 10.547405025 x = 10.547405025 Simplifying x = 10.547405025Subproblem 2
x + -5.25 = -5.297405025 Simplifying x + -5.25 = -5.297405025 Reorder the terms: -5.25 + x = -5.297405025 Solving -5.25 + x = -5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -5.297405025 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -5.297405025 + 5.25 x = -5.297405025 + 5.25 Combine like terms: -5.297405025 + 5.25 = -0.047405025 x = -0.047405025 Simplifying x = -0.047405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.547405025, -0.047405025}
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