4x^2-36x+59=0

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Solution for 4x^2-36x+59=0 equation:


Simplifying
4x2 + -36x + 59 = 0

Reorder the terms:
59 + -36x + 4x2 = 0

Solving
59 + -36x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
14.75 + -9x + x2 = 0

Move the constant term to the right:

Add '-14.75' to each side of the equation.
14.75 + -9x + -14.75 + x2 = 0 + -14.75

Reorder the terms:
14.75 + -14.75 + -9x + x2 = 0 + -14.75

Combine like terms: 14.75 + -14.75 = 0.00
0.00 + -9x + x2 = 0 + -14.75
-9x + x2 = 0 + -14.75

Combine like terms: 0 + -14.75 = -14.75
-9x + x2 = -14.75

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -14.75 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -14.75 + 20.25

Combine like terms: -14.75 + 20.25 = 5.5
20.25 + -9x + x2 = 5.5

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.34520788 and -2.34520788.

Subproblem 1

x + -4.5 = 2.34520788 Simplifying x + -4.5 = 2.34520788 Reorder the terms: -4.5 + x = 2.34520788 Solving -4.5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.34520788 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.34520788 + 4.5 x = 2.34520788 + 4.5 Combine like terms: 2.34520788 + 4.5 = 6.84520788 x = 6.84520788 Simplifying x = 6.84520788

Subproblem 2

x + -4.5 = -2.34520788 Simplifying x + -4.5 = -2.34520788 Reorder the terms: -4.5 + x = -2.34520788 Solving -4.5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.34520788 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.34520788 + 4.5 x = -2.34520788 + 4.5 Combine like terms: -2.34520788 + 4.5 = 2.15479212 x = 2.15479212 Simplifying x = 2.15479212

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.84520788, 2.15479212}

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