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Simplifying 0 = -12x2 + -120x + 209 Reorder the terms: 0 = 209 + -120x + -12x2 Solving 0 = 209 + -120x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -209 = -209 -209 + 120x + 12x2 = 209 + -120x + -12x2 + -209 + 120x + 12x2 Reorder the terms: -209 + 120x + 12x2 = 209 + -209 + -120x + 120x + -12x2 + 12x2 Combine like terms: 209 + -209 = 0 -209 + 120x + 12x2 = 0 + -120x + 120x + -12x2 + 12x2 -209 + 120x + 12x2 = -120x + 120x + -12x2 + 12x2 Combine like terms: -120x + 120x = 0 -209 + 120x + 12x2 = 0 + -12x2 + 12x2 -209 + 120x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -209 + 120x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -17.41666667 + 10x + x2 = 0 Move the constant term to the right: Add '17.41666667' to each side of the equation. -17.41666667 + 10x + 17.41666667 + x2 = 0 + 17.41666667 Reorder the terms: -17.41666667 + 17.41666667 + 10x + x2 = 0 + 17.41666667 Combine like terms: -17.41666667 + 17.41666667 = 0.00000000 0.00000000 + 10x + x2 = 0 + 17.41666667 10x + x2 = 0 + 17.41666667 Combine like terms: 0 + 17.41666667 = 17.41666667 10x + x2 = 17.41666667 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 17.41666667 + 25 Reorder the terms: 25 + 10x + x2 = 17.41666667 + 25 Combine like terms: 17.41666667 + 25 = 42.41666667 25 + 10x + x2 = 42.41666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 42.41666667 Calculate the square root of the right side: 6.512807894 Break this problem into two subproblems by setting (x + 5) equal to 6.512807894 and -6.512807894.Subproblem 1
x + 5 = 6.512807894 Simplifying x + 5 = 6.512807894 Reorder the terms: 5 + x = 6.512807894 Solving 5 + x = 6.512807894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.512807894 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.512807894 + -5 x = 6.512807894 + -5 Combine like terms: 6.512807894 + -5 = 1.512807894 x = 1.512807894 Simplifying x = 1.512807894Subproblem 2
x + 5 = -6.512807894 Simplifying x + 5 = -6.512807894 Reorder the terms: 5 + x = -6.512807894 Solving 5 + x = -6.512807894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.512807894 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.512807894 + -5 x = -6.512807894 + -5 Combine like terms: -6.512807894 + -5 = -11.512807894 x = -11.512807894 Simplifying x = -11.512807894Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.512807894, -11.512807894}
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