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Simplifying 1.1x2 + -2.1x + -1 = 0 Reorder the terms: -1 + -2.1x + 1.1x2 = 0 Solving -1 + -2.1x + 1.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.1 the coefficient of the squared term: Divide each side by '1.1'. -0.9090909091 + -1.909090909x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -1.909090909x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -1.909090909x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -1.909090909x + x2 = 0 + 0.9090909091 -1.909090909x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -1.909090909x + x2 = 0.9090909091 The x term is -1.909090909x. Take half its coefficient (-0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. -1.909090909x + 0.9111570247 + x2 = 0.9090909091 + 0.9111570247 Reorder the terms: 0.9111570247 + -1.909090909x + x2 = 0.9090909091 + 0.9111570247 Combine like terms: 0.9090909091 + 0.9111570247 = 1.8202479338 0.9111570247 + -1.909090909x + x2 = 1.8202479338 Factor a perfect square on the left side: (x + -0.9545454545)(x + -0.9545454545) = 1.8202479338 Calculate the square root of the right side: 1.349165644 Break this problem into two subproblems by setting (x + -0.9545454545) equal to 1.349165644 and -1.349165644.Subproblem 1
x + -0.9545454545 = 1.349165644 Simplifying x + -0.9545454545 = 1.349165644 Reorder the terms: -0.9545454545 + x = 1.349165644 Solving -0.9545454545 + x = 1.349165644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = 1.349165644 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = 1.349165644 + 0.9545454545 x = 1.349165644 + 0.9545454545 Combine like terms: 1.349165644 + 0.9545454545 = 2.3037110985 x = 2.3037110985 Simplifying x = 2.3037110985Subproblem 2
x + -0.9545454545 = -1.349165644 Simplifying x + -0.9545454545 = -1.349165644 Reorder the terms: -0.9545454545 + x = -1.349165644 Solving -0.9545454545 + x = -1.349165644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = -1.349165644 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = -1.349165644 + 0.9545454545 x = -1.349165644 + 0.9545454545 Combine like terms: -1.349165644 + 0.9545454545 = -0.3946201895 x = -0.3946201895 Simplifying x = -0.3946201895Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3037110985, -0.3946201895}
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