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Simplifying 9x2 + -64x + 4 = 0 Reorder the terms: 4 + -64x + 9x2 = 0 Solving 4 + -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'. 0.4444444444 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -7.111111111x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -7.111111111x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -7.111111111x + x2 = 0 + -0.4444444444 -7.111111111x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -7.111111111x + x2 = -0.4444444444 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 = -0.4444444444 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = -0.4444444444 + 12.64197531 Combine like terms: -0.4444444444 + 12.64197531 = 12.1975308656 12.64197531 + -7.111111111x + x2 = 12.1975308656 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 12.1975308656 Calculate the square root of the right side: 3.492496366 Break this problem into two subproblems by setting (x + -3.555555556) equal to 3.492496366 and -3.492496366.Subproblem 1
x + -3.555555556 = 3.492496366 Simplifying x + -3.555555556 = 3.492496366 Reorder the terms: -3.555555556 + x = 3.492496366 Solving -3.555555556 + x = 3.492496366 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 = 3.492496366 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 3.492496366 + 3.555555556 x = 3.492496366 + 3.555555556 Combine like terms: 3.492496366 + 3.555555556 = 7.048051922 x = 7.048051922 Simplifying x = 7.048051922Subproblem 2
x + -3.555555556 = -3.492496366 Simplifying x + -3.555555556 = -3.492496366 Reorder the terms: -3.555555556 + x = -3.492496366 Solving -3.555555556 + x = -3.492496366 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 = -3.492496366 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -3.492496366 + 3.555555556 x = -3.492496366 + 3.555555556 Combine like terms: -3.492496366 + 3.555555556 = 0.06305919 x = 0.06305919 Simplifying x = 0.06305919Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.048051922, 0.06305919}
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