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Simplifying 11x2 + 73x + -138 = 0 Reorder the terms: -138 + 73x + 11x2 = 0 Solving -138 + 73x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -12.54545455 + 6.636363636x + x2 = 0 Move the constant term to the right: Add '12.54545455' to each side of the equation. -12.54545455 + 6.636363636x + 12.54545455 + x2 = 0 + 12.54545455 Reorder the terms: -12.54545455 + 12.54545455 + 6.636363636x + x2 = 0 + 12.54545455 Combine like terms: -12.54545455 + 12.54545455 = 0.00000000 0.00000000 + 6.636363636x + x2 = 0 + 12.54545455 6.636363636x + x2 = 0 + 12.54545455 Combine like terms: 0 + 12.54545455 = 12.54545455 6.636363636x + x2 = 12.54545455 The x term is 6.636363636x. Take half its coefficient (3.318181818). Square it (11.01033058) and add it to both sides. Add '11.01033058' to each side of the equation. 6.636363636x + 11.01033058 + x2 = 12.54545455 + 11.01033058 Reorder the terms: 11.01033058 + 6.636363636x + x2 = 12.54545455 + 11.01033058 Combine like terms: 12.54545455 + 11.01033058 = 23.55578513 11.01033058 + 6.636363636x + x2 = 23.55578513 Factor a perfect square on the left side: (x + 3.318181818)(x + 3.318181818) = 23.55578513 Calculate the square root of the right side: 4.853430244 Break this problem into two subproblems by setting (x + 3.318181818) equal to 4.853430244 and -4.853430244.Subproblem 1
x + 3.318181818 = 4.853430244 Simplifying x + 3.318181818 = 4.853430244 Reorder the terms: 3.318181818 + x = 4.853430244 Solving 3.318181818 + x = 4.853430244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.318181818' to each side of the equation. 3.318181818 + -3.318181818 + x = 4.853430244 + -3.318181818 Combine like terms: 3.318181818 + -3.318181818 = 0.000000000 0.000000000 + x = 4.853430244 + -3.318181818 x = 4.853430244 + -3.318181818 Combine like terms: 4.853430244 + -3.318181818 = 1.535248426 x = 1.535248426 Simplifying x = 1.535248426Subproblem 2
x + 3.318181818 = -4.853430244 Simplifying x + 3.318181818 = -4.853430244 Reorder the terms: 3.318181818 + x = -4.853430244 Solving 3.318181818 + x = -4.853430244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.318181818' to each side of the equation. 3.318181818 + -3.318181818 + x = -4.853430244 + -3.318181818 Combine like terms: 3.318181818 + -3.318181818 = 0.000000000 0.000000000 + x = -4.853430244 + -3.318181818 x = -4.853430244 + -3.318181818 Combine like terms: -4.853430244 + -3.318181818 = -8.171612062 x = -8.171612062 Simplifying x = -8.171612062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.535248426, -8.171612062}
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