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Simplifying 11x2 + 40x = 80 Reorder the terms: 40x + 11x2 = 80 Solving 40x + 11x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 40x + 11x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 40x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -7.272727273 + 3.636363636x + x2 = 0 Move the constant term to the right: Add '7.272727273' to each side of the equation. -7.272727273 + 3.636363636x + 7.272727273 + x2 = 0 + 7.272727273 Reorder the terms: -7.272727273 + 7.272727273 + 3.636363636x + x2 = 0 + 7.272727273 Combine like terms: -7.272727273 + 7.272727273 = 0.000000000 0.000000000 + 3.636363636x + x2 = 0 + 7.272727273 3.636363636x + x2 = 0 + 7.272727273 Combine like terms: 0 + 7.272727273 = 7.272727273 3.636363636x + x2 = 7.272727273 The x term is 3.636363636x. Take half its coefficient (1.818181818). Square it (3.305785123) and add it to both sides. Add '3.305785123' to each side of the equation. 3.636363636x + 3.305785123 + x2 = 7.272727273 + 3.305785123 Reorder the terms: 3.305785123 + 3.636363636x + x2 = 7.272727273 + 3.305785123 Combine like terms: 7.272727273 + 3.305785123 = 10.578512396 3.305785123 + 3.636363636x + x2 = 10.578512396 Factor a perfect square on the left side: (x + 1.818181818)(x + 1.818181818) = 10.578512396 Calculate the square root of the right side: 3.252462513 Break this problem into two subproblems by setting (x + 1.818181818) equal to 3.252462513 and -3.252462513.Subproblem 1
x + 1.818181818 = 3.252462513 Simplifying x + 1.818181818 = 3.252462513 Reorder the terms: 1.818181818 + x = 3.252462513 Solving 1.818181818 + x = 3.252462513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = 3.252462513 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = 3.252462513 + -1.818181818 x = 3.252462513 + -1.818181818 Combine like terms: 3.252462513 + -1.818181818 = 1.434280695 x = 1.434280695 Simplifying x = 1.434280695Subproblem 2
x + 1.818181818 = -3.252462513 Simplifying x + 1.818181818 = -3.252462513 Reorder the terms: 1.818181818 + x = -3.252462513 Solving 1.818181818 + x = -3.252462513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = -3.252462513 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = -3.252462513 + -1.818181818 x = -3.252462513 + -1.818181818 Combine like terms: -3.252462513 + -1.818181818 = -5.070644331 x = -5.070644331 Simplifying x = -5.070644331Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.434280695, -5.070644331}
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