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Simplifying 11x2 + -50x + -21 = 0 Reorder the terms: -21 + -50x + 11x2 = 0 Solving -21 + -50x + 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'. -1.909090909 + -4.545454545x + x2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + -4.545454545x + 1.909090909 + x2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + -4.545454545x + x2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + -4.545454545x + x2 = 0 + 1.909090909 -4.545454545x + x2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 -4.545454545x + x2 = 1.909090909 The x term is -4.545454545x. Take half its coefficient (-2.272727273). Square it (5.165289257) and add it to both sides. Add '5.165289257' to each side of the equation. -4.545454545x + 5.165289257 + x2 = 1.909090909 + 5.165289257 Reorder the terms: 5.165289257 + -4.545454545x + x2 = 1.909090909 + 5.165289257 Combine like terms: 1.909090909 + 5.165289257 = 7.074380166 5.165289257 + -4.545454545x + x2 = 7.074380166 Factor a perfect square on the left side: (x + -2.272727273)(x + -2.272727273) = 7.074380166 Calculate the square root of the right side: 2.659770698 Break this problem into two subproblems by setting (x + -2.272727273) equal to 2.659770698 and -2.659770698.Subproblem 1
x + -2.272727273 = 2.659770698 Simplifying x + -2.272727273 = 2.659770698 Reorder the terms: -2.272727273 + x = 2.659770698 Solving -2.272727273 + x = 2.659770698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + x = 2.659770698 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + x = 2.659770698 + 2.272727273 x = 2.659770698 + 2.272727273 Combine like terms: 2.659770698 + 2.272727273 = 4.932497971 x = 4.932497971 Simplifying x = 4.932497971Subproblem 2
x + -2.272727273 = -2.659770698 Simplifying x + -2.272727273 = -2.659770698 Reorder the terms: -2.272727273 + x = -2.659770698 Solving -2.272727273 + x = -2.659770698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + x = -2.659770698 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + x = -2.659770698 + 2.272727273 x = -2.659770698 + 2.272727273 Combine like terms: -2.659770698 + 2.272727273 = -0.387043425 x = -0.387043425 Simplifying x = -0.387043425Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.932497971, -0.387043425}
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