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Simplifying 13x2 + -71x + -2 = 0 Reorder the terms: -2 + -71x + 13x2 = 0 Solving -2 + -71x + 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'. -0.1538461538 + -5.461538462x + x2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -5.461538462x + 0.1538461538 + x2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -5.461538462x + x2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -5.461538462x + x2 = 0 + 0.1538461538 -5.461538462x + x2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -5.461538462x + x2 = 0.1538461538 The x term is -5.461538462x. Take half its coefficient (-2.730769231). Square it (7.457100593) and add it to both sides. Add '7.457100593' to each side of the equation. -5.461538462x + 7.457100593 + x2 = 0.1538461538 + 7.457100593 Reorder the terms: 7.457100593 + -5.461538462x + x2 = 0.1538461538 + 7.457100593 Combine like terms: 0.1538461538 + 7.457100593 = 7.6109467468 7.457100593 + -5.461538462x + x2 = 7.6109467468 Factor a perfect square on the left side: (x + -2.730769231)(x + -2.730769231) = 7.6109467468 Calculate the square root of the right side: 2.758794437 Break this problem into two subproblems by setting (x + -2.730769231) equal to 2.758794437 and -2.758794437.Subproblem 1
x + -2.730769231 = 2.758794437 Simplifying x + -2.730769231 = 2.758794437 Reorder the terms: -2.730769231 + x = 2.758794437 Solving -2.730769231 + x = 2.758794437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.730769231' to each side of the equation. -2.730769231 + 2.730769231 + x = 2.758794437 + 2.730769231 Combine like terms: -2.730769231 + 2.730769231 = 0.000000000 0.000000000 + x = 2.758794437 + 2.730769231 x = 2.758794437 + 2.730769231 Combine like terms: 2.758794437 + 2.730769231 = 5.489563668 x = 5.489563668 Simplifying x = 5.489563668Subproblem 2
x + -2.730769231 = -2.758794437 Simplifying x + -2.730769231 = -2.758794437 Reorder the terms: -2.730769231 + x = -2.758794437 Solving -2.730769231 + x = -2.758794437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.730769231' to each side of the equation. -2.730769231 + 2.730769231 + x = -2.758794437 + 2.730769231 Combine like terms: -2.730769231 + 2.730769231 = 0.000000000 0.000000000 + x = -2.758794437 + 2.730769231 x = -2.758794437 + 2.730769231 Combine like terms: -2.758794437 + 2.730769231 = -0.028025206 x = -0.028025206 Simplifying x = -0.028025206Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.489563668, -0.028025206}
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