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Simplifying 11x2 + -22x + 10 = 0 Reorder the terms: 10 + -22x + 11x2 = 0 Solving 10 + -22x + 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'. 0.9090909091 + -2x + x2 = 0 Move the constant term to the right: Add '-0.9090909091' to each side of the equation. 0.9090909091 + -2x + -0.9090909091 + x2 = 0 + -0.9090909091 Reorder the terms: 0.9090909091 + -0.9090909091 + -2x + x2 = 0 + -0.9090909091 Combine like terms: 0.9090909091 + -0.9090909091 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.9090909091 -2x + x2 = 0 + -0.9090909091 Combine like terms: 0 + -0.9090909091 = -0.9090909091 -2x + x2 = -0.9090909091 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.9090909091 + 1 Reorder the terms: 1 + -2x + x2 = -0.9090909091 + 1 Combine like terms: -0.9090909091 + 1 = 0.0909090909 1 + -2x + x2 = 0.0909090909 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.0909090909 Calculate the square root of the right side: 0.301511345 Break this problem into two subproblems by setting (x + -1) equal to 0.301511345 and -0.301511345.Subproblem 1
x + -1 = 0.301511345 Simplifying x + -1 = 0.301511345 Reorder the terms: -1 + x = 0.301511345 Solving -1 + x = 0.301511345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.301511345 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.301511345 + 1 x = 0.301511345 + 1 Combine like terms: 0.301511345 + 1 = 1.301511345 x = 1.301511345 Simplifying x = 1.301511345Subproblem 2
x + -1 = -0.301511345 Simplifying x + -1 = -0.301511345 Reorder the terms: -1 + x = -0.301511345 Solving -1 + x = -0.301511345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.301511345 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.301511345 + 1 x = -0.301511345 + 1 Combine like terms: -0.301511345 + 1 = 0.698488655 x = 0.698488655 Simplifying x = 0.698488655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.301511345, 0.698488655}
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