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Simplifying x(21 + -2x) = 21 (21 * x + -2x * x) = 21 (21x + -2x2) = 21 Solving 21x + -2x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 21x + -2x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 21x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 10.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -10.5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -10.5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -10.5x + x2 = 0 + -10.5 -10.5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -10.5x + x2 = -10.5 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 = -10.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -10.5 + 27.5625 Combine like terms: -10.5 + 27.5625 = 17.0625 27.5625 + -10.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + -5.25) equal to 4.13067791 and -4.13067791.Subproblem 1
x + -5.25 = 4.13067791 Simplifying x + -5.25 = 4.13067791 Reorder the terms: -5.25 + x = 4.13067791 Solving -5.25 + x = 4.13067791 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 = 4.13067791 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.13067791 + 5.25 x = 4.13067791 + 5.25 Combine like terms: 4.13067791 + 5.25 = 9.38067791 x = 9.38067791 Simplifying x = 9.38067791Subproblem 2
x + -5.25 = -4.13067791 Simplifying x + -5.25 = -4.13067791 Reorder the terms: -5.25 + x = -4.13067791 Solving -5.25 + x = -4.13067791 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 = -4.13067791 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.13067791 + 5.25 x = -4.13067791 + 5.25 Combine like terms: -4.13067791 + 5.25 = 1.11932209 x = 1.11932209 Simplifying x = 1.11932209Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.38067791, 1.11932209}
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