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Simplifying 9x2 + -24x + 16 = 11 Reorder the terms: 16 + -24x + 9x2 = 11 Solving 16 + -24x + 9x2 = 11 Solving for variable 'x'. Reorder the terms: 16 + -11 + -24x + 9x2 = 11 + -11 Combine like terms: 16 + -11 = 5 5 + -24x + 9x2 = 11 + -11 Combine like terms: 11 + -11 = 0 5 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -2.666666667x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -2.666666667x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + -0.5555555556 -2.666666667x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -2.666666667x + x2 = -0.5555555556 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -0.5555555556 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -0.5555555556 + 1.777777780 Combine like terms: -0.5555555556 + 1.777777780 = 1.2222222244 1.777777780 + -2.666666667x + x2 = 1.2222222244 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.2222222244 Calculate the square root of the right side: 1.105541598 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.105541598 and -1.105541598.Subproblem 1
x + -1.333333334 = 1.105541598 Simplifying x + -1.333333334 = 1.105541598 Reorder the terms: -1.333333334 + x = 1.105541598 Solving -1.333333334 + x = 1.105541598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.105541598 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.105541598 + 1.333333334 x = 1.105541598 + 1.333333334 Combine like terms: 1.105541598 + 1.333333334 = 2.438874932 x = 2.438874932 Simplifying x = 2.438874932Subproblem 2
x + -1.333333334 = -1.105541598 Simplifying x + -1.333333334 = -1.105541598 Reorder the terms: -1.333333334 + x = -1.105541598 Solving -1.333333334 + x = -1.105541598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.105541598 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.105541598 + 1.333333334 x = -1.105541598 + 1.333333334 Combine like terms: -1.105541598 + 1.333333334 = 0.227791736 x = 0.227791736 Simplifying x = 0.227791736Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.438874932, 0.227791736}
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