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Simplifying 0 = -3x2 + 21x + 50 Reorder the terms: 0 = 50 + 21x + -3x2 Solving 0 = 50 + 21x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + -21x + 3x2 = 50 + 21x + -3x2 + -50 + -21x + 3x2 Reorder the terms: -50 + -21x + 3x2 = 50 + -50 + 21x + -21x + -3x2 + 3x2 Combine like terms: 50 + -50 = 0 -50 + -21x + 3x2 = 0 + 21x + -21x + -3x2 + 3x2 -50 + -21x + 3x2 = 21x + -21x + -3x2 + 3x2 Combine like terms: 21x + -21x = 0 -50 + -21x + 3x2 = 0 + -3x2 + 3x2 -50 + -21x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -50 + -21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -7x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -7x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -7x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -7x + x2 = 0 + 16.66666667 -7x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -7x + x2 = 16.66666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 16.66666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 16.66666667 + 12.25 Combine like terms: 16.66666667 + 12.25 = 28.91666667 12.25 + -7x + x2 = 28.91666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 28.91666667 Calculate the square root of the right side: 5.377421935 Break this problem into two subproblems by setting (x + -3.5) equal to 5.377421935 and -5.377421935.Subproblem 1
x + -3.5 = 5.377421935 Simplifying x + -3.5 = 5.377421935 Reorder the terms: -3.5 + x = 5.377421935 Solving -3.5 + x = 5.377421935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.377421935 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.377421935 + 3.5 x = 5.377421935 + 3.5 Combine like terms: 5.377421935 + 3.5 = 8.877421935 x = 8.877421935 Simplifying x = 8.877421935Subproblem 2
x + -3.5 = -5.377421935 Simplifying x + -3.5 = -5.377421935 Reorder the terms: -3.5 + x = -5.377421935 Solving -3.5 + x = -5.377421935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.377421935 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.377421935 + 3.5 x = -5.377421935 + 3.5 Combine like terms: -5.377421935 + 3.5 = -1.877421935 x = -1.877421935 Simplifying x = -1.877421935Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.877421935, -1.877421935}
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