0=-2x^2+29x-18

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Solution for 0=-2x^2+29x-18 equation:


Simplifying
0 = -2x2 + 29x + -18

Reorder the terms:
0 = -18 + 29x + -2x2

Solving
0 = -18 + 29x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 18 = 18
18 + -29x + 2x2 = -18 + 29x + -2x2 + 18 + -29x + 2x2

Reorder the terms:
18 + -29x + 2x2 = -18 + 18 + 29x + -29x + -2x2 + 2x2

Combine like terms: -18 + 18 = 0
18 + -29x + 2x2 = 0 + 29x + -29x + -2x2 + 2x2
18 + -29x + 2x2 = 29x + -29x + -2x2 + 2x2

Combine like terms: 29x + -29x = 0
18 + -29x + 2x2 = 0 + -2x2 + 2x2
18 + -29x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
18 + -29x + 2x2 = 0

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

Divide each side by '2'.
9 + -14.5x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -14.5x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -14.5x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -14.5x + x2 = 0 + -9
-14.5x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-14.5x + x2 = -9

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 = -9 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = -9 + 52.5625

Combine like terms: -9 + 52.5625 = 43.5625
52.5625 + -14.5x + x2 = 43.5625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 43.5625

Calculate the square root of the right side: 6.600189391

Break this problem into two subproblems by setting 
(x + -7.25) equal to 6.600189391 and -6.600189391.

Subproblem 1

x + -7.25 = 6.600189391 Simplifying x + -7.25 = 6.600189391 Reorder the terms: -7.25 + x = 6.600189391 Solving -7.25 + x = 6.600189391 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 = 6.600189391 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 6.600189391 + 7.25 x = 6.600189391 + 7.25 Combine like terms: 6.600189391 + 7.25 = 13.850189391 x = 13.850189391 Simplifying x = 13.850189391

Subproblem 2

x + -7.25 = -6.600189391 Simplifying x + -7.25 = -6.600189391 Reorder the terms: -7.25 + x = -6.600189391 Solving -7.25 + x = -6.600189391 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 = -6.600189391 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -6.600189391 + 7.25 x = -6.600189391 + 7.25 Combine like terms: -6.600189391 + 7.25 = 0.649810609 x = 0.649810609 Simplifying x = 0.649810609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.850189391, 0.649810609}

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