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Simplifying 9x2 + -64x + 45 = 0 Reorder the terms: 45 + -64x + 9x2 = 0 Solving 45 + -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'. 5 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7.111111111x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7.111111111x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7.111111111x + x2 = 0 + -5 -7.111111111x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7.111111111x + x2 = -5 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 = -5 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = -5 + 12.64197531 Combine like terms: -5 + 12.64197531 = 7.64197531 12.64197531 + -7.111111111x + x2 = 7.64197531 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 7.64197531 Calculate the square root of the right side: 2.76441229 Break this problem into two subproblems by setting (x + -3.555555556) equal to 2.76441229 and -2.76441229.Subproblem 1
x + -3.555555556 = 2.76441229 Simplifying x + -3.555555556 = 2.76441229 Reorder the terms: -3.555555556 + x = 2.76441229 Solving -3.555555556 + x = 2.76441229 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 = 2.76441229 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 2.76441229 + 3.555555556 x = 2.76441229 + 3.555555556 Combine like terms: 2.76441229 + 3.555555556 = 6.319967846 x = 6.319967846 Simplifying x = 6.319967846Subproblem 2
x + -3.555555556 = -2.76441229 Simplifying x + -3.555555556 = -2.76441229 Reorder the terms: -3.555555556 + x = -2.76441229 Solving -3.555555556 + x = -2.76441229 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 = -2.76441229 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -2.76441229 + 3.555555556 x = -2.76441229 + 3.555555556 Combine like terms: -2.76441229 + 3.555555556 = 0.791143266 x = 0.791143266 Simplifying x = 0.791143266Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.319967846, 0.791143266}
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