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Simplifying 13x2 + -42x = 147 Reorder the terms: -42x + 13x2 = 147 Solving -42x + 13x2 = 147 Solving for variable 'x'. Reorder the terms: -147 + -42x + 13x2 = 147 + -147 Combine like terms: 147 + -147 = 0 -147 + -42x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -11.30769231 + -3.230769231x + x2 = 0 Move the constant term to the right: Add '11.30769231' to each side of the equation. -11.30769231 + -3.230769231x + 11.30769231 + x2 = 0 + 11.30769231 Reorder the terms: -11.30769231 + 11.30769231 + -3.230769231x + x2 = 0 + 11.30769231 Combine like terms: -11.30769231 + 11.30769231 = 0.00000000 0.00000000 + -3.230769231x + x2 = 0 + 11.30769231 -3.230769231x + x2 = 0 + 11.30769231 Combine like terms: 0 + 11.30769231 = 11.30769231 -3.230769231x + x2 = 11.30769231 The x term is -3.230769231x. Take half its coefficient (-1.615384616). Square it (2.609467458) and add it to both sides. Add '2.609467458' to each side of the equation. -3.230769231x + 2.609467458 + x2 = 11.30769231 + 2.609467458 Reorder the terms: 2.609467458 + -3.230769231x + x2 = 11.30769231 + 2.609467458 Combine like terms: 11.30769231 + 2.609467458 = 13.917159768 2.609467458 + -3.230769231x + x2 = 13.917159768 Factor a perfect square on the left side: (x + -1.615384616)(x + -1.615384616) = 13.917159768 Calculate the square root of the right side: 3.730570971 Break this problem into two subproblems by setting (x + -1.615384616) equal to 3.730570971 and -3.730570971.Subproblem 1
x + -1.615384616 = 3.730570971 Simplifying x + -1.615384616 = 3.730570971 Reorder the terms: -1.615384616 + x = 3.730570971 Solving -1.615384616 + x = 3.730570971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.615384616' to each side of the equation. -1.615384616 + 1.615384616 + x = 3.730570971 + 1.615384616 Combine like terms: -1.615384616 + 1.615384616 = 0.000000000 0.000000000 + x = 3.730570971 + 1.615384616 x = 3.730570971 + 1.615384616 Combine like terms: 3.730570971 + 1.615384616 = 5.345955587 x = 5.345955587 Simplifying x = 5.345955587Subproblem 2
x + -1.615384616 = -3.730570971 Simplifying x + -1.615384616 = -3.730570971 Reorder the terms: -1.615384616 + x = -3.730570971 Solving -1.615384616 + x = -3.730570971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.615384616' to each side of the equation. -1.615384616 + 1.615384616 + x = -3.730570971 + 1.615384616 Combine like terms: -1.615384616 + 1.615384616 = 0.000000000 0.000000000 + x = -3.730570971 + 1.615384616 x = -3.730570971 + 1.615384616 Combine like terms: -3.730570971 + 1.615384616 = -2.115186355 x = -2.115186355 Simplifying x = -2.115186355Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.345955587, -2.115186355}
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