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Simplifying 2x2 + -21x + 13 = 0 Reorder the terms: 13 + -21x + 2x2 = 0 Solving 13 + -21x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -10.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -10.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -10.5x + x2 = 0 + -6.5 -10.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -10.5x + x2 = -6.5 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 = -6.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -6.5 + 27.5625 Combine like terms: -6.5 + 27.5625 = 21.0625 27.5625 + -10.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + -5.25) equal to 4.589389938 and -4.589389938.Subproblem 1
x + -5.25 = 4.589389938 Simplifying x + -5.25 = 4.589389938 Reorder the terms: -5.25 + x = 4.589389938 Solving -5.25 + x = 4.589389938 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 = 4.589389938 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.589389938 + 5.25 x = 4.589389938 + 5.25 Combine like terms: 4.589389938 + 5.25 = 9.839389938 x = 9.839389938 Simplifying x = 9.839389938Subproblem 2
x + -5.25 = -4.589389938 Simplifying x + -5.25 = -4.589389938 Reorder the terms: -5.25 + x = -4.589389938 Solving -5.25 + x = -4.589389938 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 = -4.589389938 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.589389938 + 5.25 x = -4.589389938 + 5.25 Combine like terms: -4.589389938 + 5.25 = 0.660610062 x = 0.660610062 Simplifying x = 0.660610062Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.839389938, 0.660610062}
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