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Simplifying 13x2 + 16x + -11 = 0 Reorder the terms: -11 + 16x + 13x2 = 0 Solving -11 + 16x + 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'. -0.8461538462 + 1.230769231x + x2 = 0 Move the constant term to the right: Add '0.8461538462' to each side of the equation. -0.8461538462 + 1.230769231x + 0.8461538462 + x2 = 0 + 0.8461538462 Reorder the terms: -0.8461538462 + 0.8461538462 + 1.230769231x + x2 = 0 + 0.8461538462 Combine like terms: -0.8461538462 + 0.8461538462 = 0.0000000000 0.0000000000 + 1.230769231x + x2 = 0 + 0.8461538462 1.230769231x + x2 = 0 + 0.8461538462 Combine like terms: 0 + 0.8461538462 = 0.8461538462 1.230769231x + x2 = 0.8461538462 The x term is 1.230769231x. Take half its coefficient (0.6153846155). Square it (0.3786982250) and add it to both sides. Add '0.3786982250' to each side of the equation. 1.230769231x + 0.3786982250 + x2 = 0.8461538462 + 0.3786982250 Reorder the terms: 0.3786982250 + 1.230769231x + x2 = 0.8461538462 + 0.3786982250 Combine like terms: 0.8461538462 + 0.3786982250 = 1.2248520712 0.3786982250 + 1.230769231x + x2 = 1.2248520712 Factor a perfect square on the left side: (x + 0.6153846155)(x + 0.6153846155) = 1.2248520712 Calculate the square root of the right side: 1.106730352 Break this problem into two subproblems by setting (x + 0.6153846155) equal to 1.106730352 and -1.106730352.Subproblem 1
x + 0.6153846155 = 1.106730352 Simplifying x + 0.6153846155 = 1.106730352 Reorder the terms: 0.6153846155 + x = 1.106730352 Solving 0.6153846155 + x = 1.106730352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6153846155' to each side of the equation. 0.6153846155 + -0.6153846155 + x = 1.106730352 + -0.6153846155 Combine like terms: 0.6153846155 + -0.6153846155 = 0.0000000000 0.0000000000 + x = 1.106730352 + -0.6153846155 x = 1.106730352 + -0.6153846155 Combine like terms: 1.106730352 + -0.6153846155 = 0.4913457365 x = 0.4913457365 Simplifying x = 0.4913457365Subproblem 2
x + 0.6153846155 = -1.106730352 Simplifying x + 0.6153846155 = -1.106730352 Reorder the terms: 0.6153846155 + x = -1.106730352 Solving 0.6153846155 + x = -1.106730352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6153846155' to each side of the equation. 0.6153846155 + -0.6153846155 + x = -1.106730352 + -0.6153846155 Combine like terms: 0.6153846155 + -0.6153846155 = 0.0000000000 0.0000000000 + x = -1.106730352 + -0.6153846155 x = -1.106730352 + -0.6153846155 Combine like terms: -1.106730352 + -0.6153846155 = -1.7221149675 x = -1.7221149675 Simplifying x = -1.7221149675Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4913457365, -1.7221149675}
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