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Simplifying 11x2 + -20 = -10x Reorder the terms: -20 + 11x2 = -10x Solving -20 + 11x2 = -10x Solving for variable 'x'. Reorder the terms: -20 + 10x + 11x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -20 + 10x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.818181818 + 0.9090909091x + x2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + 0.9090909091x + 1.818181818 + x2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + 0.9090909091x + x2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + 0.9090909091x + x2 = 0 + 1.818181818 0.9090909091x + x2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 0.9090909091x + x2 = 1.818181818 The x term is 0.9090909091x. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091x + 0.2066115703 + x2 = 1.818181818 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091x + x2 = 1.818181818 + 0.2066115703 Combine like terms: 1.818181818 + 0.2066115703 = 2.0247933883 0.2066115703 + 0.9090909091x + x2 = 2.0247933883 Factor a perfect square on the left side: (x + 0.4545454546)(x + 0.4545454546) = 2.0247933883 Calculate the square root of the right side: 1.422952349 Break this problem into two subproblems by setting (x + 0.4545454546) equal to 1.422952349 and -1.422952349.Subproblem 1
x + 0.4545454546 = 1.422952349 Simplifying x + 0.4545454546 = 1.422952349 Reorder the terms: 0.4545454546 + x = 1.422952349 Solving 0.4545454546 + x = 1.422952349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = 1.422952349 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = 1.422952349 + -0.4545454546 x = 1.422952349 + -0.4545454546 Combine like terms: 1.422952349 + -0.4545454546 = 0.9684068944 x = 0.9684068944 Simplifying x = 0.9684068944Subproblem 2
x + 0.4545454546 = -1.422952349 Simplifying x + 0.4545454546 = -1.422952349 Reorder the terms: 0.4545454546 + x = -1.422952349 Solving 0.4545454546 + x = -1.422952349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = -1.422952349 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = -1.422952349 + -0.4545454546 x = -1.422952349 + -0.4545454546 Combine like terms: -1.422952349 + -0.4545454546 = -1.8774978036 x = -1.8774978036 Simplifying x = -1.8774978036Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9684068944, -1.8774978036}
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