9x^2-5x+16=29x

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Solution for 9x^2-5x+16=29x equation:


Simplifying
9x2 + -5x + 16 = 29x

Reorder the terms:
16 + -5x + 9x2 = 29x

Solving
16 + -5x + 9x2 = 29x

Solving for variable 'x'.

Reorder the terms:
16 + -5x + -29x + 9x2 = 29x + -29x

Combine like terms: -5x + -29x = -34x
16 + -34x + 9x2 = 29x + -29x

Combine like terms: 29x + -29x = 0
16 + -34x + 9x2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
1.777777778 + -3.777777778x + x2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + -3.777777778x + -1.777777778 + x2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + -3.777777778x + x2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + -3.777777778x + x2 = 0 + -1.777777778
-3.777777778x + x2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
-3.777777778x + x2 = -1.777777778

The x term is -3.777777778x.  Take half its coefficient (-1.888888889).
Square it (3.567901235) and add it to both sides.

Add '3.567901235' to each side of the equation.
-3.777777778x + 3.567901235 + x2 = -1.777777778 + 3.567901235

Reorder the terms:
3.567901235 + -3.777777778x + x2 = -1.777777778 + 3.567901235

Combine like terms: -1.777777778 + 3.567901235 = 1.790123457
3.567901235 + -3.777777778x + x2 = 1.790123457

Factor a perfect square on the left side:
(x + -1.888888889)(x + -1.888888889) = 1.790123457

Calculate the square root of the right side: 1.337954953

Break this problem into two subproblems by setting 
(x + -1.888888889) equal to 1.337954953 and -1.337954953.

Subproblem 1

x + -1.888888889 = 1.337954953 Simplifying x + -1.888888889 = 1.337954953 Reorder the terms: -1.888888889 + x = 1.337954953 Solving -1.888888889 + x = 1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = 1.337954953 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 1.337954953 + 1.888888889 x = 1.337954953 + 1.888888889 Combine like terms: 1.337954953 + 1.888888889 = 3.226843842 x = 3.226843842 Simplifying x = 3.226843842

Subproblem 2

x + -1.888888889 = -1.337954953 Simplifying x + -1.888888889 = -1.337954953 Reorder the terms: -1.888888889 + x = -1.337954953 Solving -1.888888889 + x = -1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = -1.337954953 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -1.337954953 + 1.888888889 x = -1.337954953 + 1.888888889 Combine like terms: -1.337954953 + 1.888888889 = 0.550933936 x = 0.550933936 Simplifying x = 0.550933936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.226843842, 0.550933936}

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