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Simplifying 9x2 + -64x + 96 = 0 Reorder the terms: 96 + -64x + 9x2 = 0 Solving 96 + -64x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 10.66666667 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + -7.111111111x + -10.66666667 + x2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + -7.111111111x + x2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + -7.111111111x + x2 = 0 + -10.66666667 -7.111111111x + x2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 -7.111111111x + x2 = -10.66666667 The x term is -7.111111111x. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111x + 12.64197531 + x2 = -10.66666667 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = -10.66666667 + 12.64197531 Combine like terms: -10.66666667 + 12.64197531 = 1.97530864 12.64197531 + -7.111111111x + x2 = 1.97530864 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 1.97530864 Calculate the square root of the right side: 1.405456737 Break this problem into two subproblems by setting (x + -3.555555556) equal to 1.405456737 and -1.405456737.Subproblem 1
x + -3.555555556 = 1.405456737 Simplifying x + -3.555555556 = 1.405456737 Reorder the terms: -3.555555556 + x = 1.405456737 Solving -3.555555556 + x = 1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = 1.405456737 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 1.405456737 + 3.555555556 x = 1.405456737 + 3.555555556 Combine like terms: 1.405456737 + 3.555555556 = 4.961012293 x = 4.961012293 Simplifying x = 4.961012293Subproblem 2
x + -3.555555556 = -1.405456737 Simplifying x + -3.555555556 = -1.405456737 Reorder the terms: -3.555555556 + x = -1.405456737 Solving -3.555555556 + x = -1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = -1.405456737 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -1.405456737 + 3.555555556 x = -1.405456737 + 3.555555556 Combine like terms: -1.405456737 + 3.555555556 = 2.150098819 x = 2.150098819 Simplifying x = 2.150098819Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.961012293, 2.150098819}
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