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Simplifying 11x2 + -6x + -21 = 0 Reorder the terms: -21 + -6x + 11x2 = 0 Solving -21 + -6x + 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 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + -0.5454545455x + 1.909090909 + x2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + -0.5454545455x + x2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + -0.5454545455x + x2 = 0 + 1.909090909 -0.5454545455x + x2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 -0.5454545455x + x2 = 1.909090909 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 1.909090909 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 1.909090909 + 0.07438016533 Combine like terms: 1.909090909 + 0.07438016533 = 1.98347107433 0.07438016533 + -0.5454545455x + x2 = 1.98347107433 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 1.98347107433 Calculate the square root of the right side: 1.40835758 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 1.40835758 and -1.40835758.Subproblem 1
x + -0.2727272728 = 1.40835758 Simplifying x + -0.2727272728 = 1.40835758 Reorder the terms: -0.2727272728 + x = 1.40835758 Solving -0.2727272728 + x = 1.40835758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 1.40835758 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 1.40835758 + 0.2727272728 x = 1.40835758 + 0.2727272728 Combine like terms: 1.40835758 + 0.2727272728 = 1.6810848528 x = 1.6810848528 Simplifying x = 1.6810848528Subproblem 2
x + -0.2727272728 = -1.40835758 Simplifying x + -0.2727272728 = -1.40835758 Reorder the terms: -0.2727272728 + x = -1.40835758 Solving -0.2727272728 + x = -1.40835758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -1.40835758 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -1.40835758 + 0.2727272728 x = -1.40835758 + 0.2727272728 Combine like terms: -1.40835758 + 0.2727272728 = -1.1356303072 x = -1.1356303072 Simplifying x = -1.1356303072Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6810848528, -1.1356303072}
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