2x^2-29x-345=0

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Solution for 2x^2-29x-345=0 equation:


Simplifying
2x2 + -29x + -345 = 0

Reorder the terms:
-345 + -29x + 2x2 = 0

Solving
-345 + -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'.
-172.5 + -14.5x + x2 = 0

Move the constant term to the right:

Add '172.5' to each side of the equation.
-172.5 + -14.5x + 172.5 + x2 = 0 + 172.5

Reorder the terms:
-172.5 + 172.5 + -14.5x + x2 = 0 + 172.5

Combine like terms: -172.5 + 172.5 = 0.0
0.0 + -14.5x + x2 = 0 + 172.5
-14.5x + x2 = 0 + 172.5

Combine like terms: 0 + 172.5 = 172.5
-14.5x + x2 = 172.5

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 = 172.5 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = 172.5 + 52.5625

Combine like terms: 172.5 + 52.5625 = 225.0625
52.5625 + -14.5x + x2 = 225.0625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 225.0625

Calculate the square root of the right side: 15.002083189

Break this problem into two subproblems by setting 
(x + -7.25) equal to 15.002083189 and -15.002083189.

Subproblem 1

x + -7.25 = 15.002083189 Simplifying x + -7.25 = 15.002083189 Reorder the terms: -7.25 + x = 15.002083189 Solving -7.25 + x = 15.002083189 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 = 15.002083189 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 15.002083189 + 7.25 x = 15.002083189 + 7.25 Combine like terms: 15.002083189 + 7.25 = 22.252083189 x = 22.252083189 Simplifying x = 22.252083189

Subproblem 2

x + -7.25 = -15.002083189 Simplifying x + -7.25 = -15.002083189 Reorder the terms: -7.25 + x = -15.002083189 Solving -7.25 + x = -15.002083189 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 = -15.002083189 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -15.002083189 + 7.25 x = -15.002083189 + 7.25 Combine like terms: -15.002083189 + 7.25 = -7.752083189 x = -7.752083189 Simplifying x = -7.752083189

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.252083189, -7.752083189}

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