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Simplifying 13x2 + -80x + -81 = 0 Reorder the terms: -81 + -80x + 13x2 = 0 Solving -81 + -80x + 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'. -6.230769231 + -6.153846154x + x2 = 0 Move the constant term to the right: Add '6.230769231' to each side of the equation. -6.230769231 + -6.153846154x + 6.230769231 + x2 = 0 + 6.230769231 Reorder the terms: -6.230769231 + 6.230769231 + -6.153846154x + x2 = 0 + 6.230769231 Combine like terms: -6.230769231 + 6.230769231 = 0.000000000 0.000000000 + -6.153846154x + x2 = 0 + 6.230769231 -6.153846154x + x2 = 0 + 6.230769231 Combine like terms: 0 + 6.230769231 = 6.230769231 -6.153846154x + x2 = 6.230769231 The x term is -6.153846154x. Take half its coefficient (-3.076923077). Square it (9.467455622) and add it to both sides. Add '9.467455622' to each side of the equation. -6.153846154x + 9.467455622 + x2 = 6.230769231 + 9.467455622 Reorder the terms: 9.467455622 + -6.153846154x + x2 = 6.230769231 + 9.467455622 Combine like terms: 6.230769231 + 9.467455622 = 15.698224853 9.467455622 + -6.153846154x + x2 = 15.698224853 Factor a perfect square on the left side: (x + -3.076923077)(x + -3.076923077) = 15.698224853 Calculate the square root of the right side: 3.962098542 Break this problem into two subproblems by setting (x + -3.076923077) equal to 3.962098542 and -3.962098542.Subproblem 1
x + -3.076923077 = 3.962098542 Simplifying x + -3.076923077 = 3.962098542 Reorder the terms: -3.076923077 + x = 3.962098542 Solving -3.076923077 + x = 3.962098542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.076923077' to each side of the equation. -3.076923077 + 3.076923077 + x = 3.962098542 + 3.076923077 Combine like terms: -3.076923077 + 3.076923077 = 0.000000000 0.000000000 + x = 3.962098542 + 3.076923077 x = 3.962098542 + 3.076923077 Combine like terms: 3.962098542 + 3.076923077 = 7.039021619 x = 7.039021619 Simplifying x = 7.039021619Subproblem 2
x + -3.076923077 = -3.962098542 Simplifying x + -3.076923077 = -3.962098542 Reorder the terms: -3.076923077 + x = -3.962098542 Solving -3.076923077 + x = -3.962098542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.076923077' to each side of the equation. -3.076923077 + 3.076923077 + x = -3.962098542 + 3.076923077 Combine like terms: -3.076923077 + 3.076923077 = 0.000000000 0.000000000 + x = -3.962098542 + 3.076923077 x = -3.962098542 + 3.076923077 Combine like terms: -3.962098542 + 3.076923077 = -0.885175465 x = -0.885175465 Simplifying x = -0.885175465Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.039021619, -0.885175465}
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