2x^2-29x+81=0

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Solution for 2x^2-29x+81=0 equation:


Simplifying
2x2 + -29x + 81 = 0

Reorder the terms:
81 + -29x + 2x2 = 0

Solving
81 + -29x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
40.5 + -14.5x + x2 = 0

Move the constant term to the right:

Add '-40.5' to each side of the equation.
40.5 + -14.5x + -40.5 + x2 = 0 + -40.5

Reorder the terms:
40.5 + -40.5 + -14.5x + x2 = 0 + -40.5

Combine like terms: 40.5 + -40.5 = 0.0
0.0 + -14.5x + x2 = 0 + -40.5
-14.5x + x2 = 0 + -40.5

Combine like terms: 0 + -40.5 = -40.5
-14.5x + x2 = -40.5

The x term is -14.5x.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5x + 52.5625 + x2 = -40.5 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = -40.5 + 52.5625

Combine like terms: -40.5 + 52.5625 = 12.0625
52.5625 + -14.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -7.25) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + -7.25 = 3.473110997 Simplifying x + -7.25 = 3.473110997 Reorder the terms: -7.25 + x = 3.473110997 Solving -7.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 3.473110997 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 3.473110997 + 7.25 x = 3.473110997 + 7.25 Combine like terms: 3.473110997 + 7.25 = 10.723110997 x = 10.723110997 Simplifying x = 10.723110997

Subproblem 2

x + -7.25 = -3.473110997 Simplifying x + -7.25 = -3.473110997 Reorder the terms: -7.25 + x = -3.473110997 Solving -7.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -3.473110997 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -3.473110997 + 7.25 x = -3.473110997 + 7.25 Combine like terms: -3.473110997 + 7.25 = 3.776889003 x = 3.776889003 Simplifying x = 3.776889003

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.723110997, 3.776889003}

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