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Simplifying 12x2 + -24x + 11 = 0 Reorder the terms: 11 + -24x + 12x2 = 0 Solving 11 + -24x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.9166666667 + -2x + x2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + -2x + -0.9166666667 + x2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + -2x + x2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.9166666667 -2x + x2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 -2x + x2 = -0.9166666667 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 = -0.9166666667 + 1 Reorder the terms: 1 + -2x + x2 = -0.9166666667 + 1 Combine like terms: -0.9166666667 + 1 = 0.0833333333 1 + -2x + x2 = 0.0833333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.0833333333 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting (x + -1) equal to 0.288675135 and -0.288675135.Subproblem 1
x + -1 = 0.288675135 Simplifying x + -1 = 0.288675135 Reorder the terms: -1 + x = 0.288675135 Solving -1 + x = 0.288675135 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 = 0.288675135 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.288675135 + 1 x = 0.288675135 + 1 Combine like terms: 0.288675135 + 1 = 1.288675135 x = 1.288675135 Simplifying x = 1.288675135Subproblem 2
x + -1 = -0.288675135 Simplifying x + -1 = -0.288675135 Reorder the terms: -1 + x = -0.288675135 Solving -1 + x = -0.288675135 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 = -0.288675135 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.288675135 + 1 x = -0.288675135 + 1 Combine like terms: -0.288675135 + 1 = 0.711324865 x = 0.711324865 Simplifying x = 0.711324865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.288675135, 0.711324865}
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