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Simplifying 0 = x2 + -21x + 50 Reorder the terms: 0 = 50 + -21x + x2 Solving 0 = 50 + -21x + x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 21x + -1x2 = 50 + -21x + x2 + -50 + 21x + -1x2 Reorder the terms: -50 + 21x + -1x2 = 50 + -50 + -21x + 21x + x2 + -1x2 Combine like terms: 50 + -50 = 0 -50 + 21x + -1x2 = 0 + -21x + 21x + x2 + -1x2 -50 + 21x + -1x2 = -21x + 21x + x2 + -1x2 Combine like terms: -21x + 21x = 0 -50 + 21x + -1x2 = 0 + x2 + -1x2 -50 + 21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + 21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -21x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -21x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -21x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -21x + x2 = 0 + -50 -21x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -21x + x2 = -50 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -50 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -50 + 110.25 Combine like terms: -50 + 110.25 = 60.25 110.25 + -21x + x2 = 60.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -10.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -10.5 = 7.762087348 Simplifying x + -10.5 = 7.762087348 Reorder the terms: -10.5 + x = 7.762087348 Solving -10.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 7.762087348 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.762087348 + 10.5 x = 7.762087348 + 10.5 Combine like terms: 7.762087348 + 10.5 = 18.262087348 x = 18.262087348 Simplifying x = 18.262087348Subproblem 2
x + -10.5 = -7.762087348 Simplifying x + -10.5 = -7.762087348 Reorder the terms: -10.5 + x = -7.762087348 Solving -10.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -7.762087348 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.762087348 + 10.5 x = -7.762087348 + 10.5 Combine like terms: -7.762087348 + 10.5 = 2.737912652 x = 2.737912652 Simplifying x = 2.737912652Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.262087348, 2.737912652}
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