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Simplifying 13x2 + -120x + 201 = 0 Reorder the terms: 201 + -120x + 13x2 = 0 Solving 201 + -120x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 15.46153846 + -9.230769231x + x2 = 0 Move the constant term to the right: Add '-15.46153846' to each side of the equation. 15.46153846 + -9.230769231x + -15.46153846 + x2 = 0 + -15.46153846 Reorder the terms: 15.46153846 + -15.46153846 + -9.230769231x + x2 = 0 + -15.46153846 Combine like terms: 15.46153846 + -15.46153846 = 0.00000000 0.00000000 + -9.230769231x + x2 = 0 + -15.46153846 -9.230769231x + x2 = 0 + -15.46153846 Combine like terms: 0 + -15.46153846 = -15.46153846 -9.230769231x + x2 = -15.46153846 The x term is -9.230769231x. Take half its coefficient (-4.615384616). Square it (21.30177515) and add it to both sides. Add '21.30177515' to each side of the equation. -9.230769231x + 21.30177515 + x2 = -15.46153846 + 21.30177515 Reorder the terms: 21.30177515 + -9.230769231x + x2 = -15.46153846 + 21.30177515 Combine like terms: -15.46153846 + 21.30177515 = 5.84023669 21.30177515 + -9.230769231x + x2 = 5.84023669 Factor a perfect square on the left side: (x + -4.615384616)(x + -4.615384616) = 5.84023669 Calculate the square root of the right side: 2.416658166 Break this problem into two subproblems by setting (x + -4.615384616) equal to 2.416658166 and -2.416658166.Subproblem 1
x + -4.615384616 = 2.416658166 Simplifying x + -4.615384616 = 2.416658166 Reorder the terms: -4.615384616 + x = 2.416658166 Solving -4.615384616 + x = 2.416658166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.615384616' to each side of the equation. -4.615384616 + 4.615384616 + x = 2.416658166 + 4.615384616 Combine like terms: -4.615384616 + 4.615384616 = 0.000000000 0.000000000 + x = 2.416658166 + 4.615384616 x = 2.416658166 + 4.615384616 Combine like terms: 2.416658166 + 4.615384616 = 7.032042782 x = 7.032042782 Simplifying x = 7.032042782Subproblem 2
x + -4.615384616 = -2.416658166 Simplifying x + -4.615384616 = -2.416658166 Reorder the terms: -4.615384616 + x = -2.416658166 Solving -4.615384616 + x = -2.416658166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.615384616' to each side of the equation. -4.615384616 + 4.615384616 + x = -2.416658166 + 4.615384616 Combine like terms: -4.615384616 + 4.615384616 = 0.000000000 0.000000000 + x = -2.416658166 + 4.615384616 x = -2.416658166 + 4.615384616 Combine like terms: -2.416658166 + 4.615384616 = 2.19872645 x = 2.19872645 Simplifying x = 2.19872645Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.032042782, 2.19872645}
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