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Simplifying x(21 + -2x) = 46 (21 * x + -2x * x) = 46 (21x + -2x2) = 46 Solving 21x + -2x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 21x + -2x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 21x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 23 + -10.5x + x2 = 0 Move the constant term to the right: Add '-23' to each side of the equation. 23 + -10.5x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -10.5x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -10.5x + x2 = 0 + -23 -10.5x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -10.5x + x2 = -23 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 = -23 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -23 + 27.5625 Combine like terms: -23 + 27.5625 = 4.5625 27.5625 + -10.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -5.25) equal to 2.136000936 and -2.136000936.Subproblem 1
x + -5.25 = 2.136000936 Simplifying x + -5.25 = 2.136000936 Reorder the terms: -5.25 + x = 2.136000936 Solving -5.25 + x = 2.136000936 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 = 2.136000936 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 2.136000936 + 5.25 x = 2.136000936 + 5.25 Combine like terms: 2.136000936 + 5.25 = 7.386000936 x = 7.386000936 Simplifying x = 7.386000936Subproblem 2
x + -5.25 = -2.136000936 Simplifying x + -5.25 = -2.136000936 Reorder the terms: -5.25 + x = -2.136000936 Solving -5.25 + x = -2.136000936 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 = -2.136000936 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -2.136000936 + 5.25 x = -2.136000936 + 5.25 Combine like terms: -2.136000936 + 5.25 = 3.113999064 x = 3.113999064 Simplifying x = 3.113999064Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.386000936, 3.113999064}
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