4x^2-36x+7=0

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Solution for 4x^2-36x+7=0 equation:


Simplifying
4x2 + -36x + 7 = 0

Reorder the terms:
7 + -36x + 4x2 = 0

Solving
7 + -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'.
1.75 + -9x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -9x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -9x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -9x + x2 = 0 + -1.75
-9x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-9x + x2 = -1.75

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 = -1.75 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -1.75 + 20.25

Combine like terms: -1.75 + 20.25 = 18.5
20.25 + -9x + x2 = 18.5

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 18.5

Calculate the square root of the right side: 4.301162634

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.301162634 and -4.301162634.

Subproblem 1

x + -4.5 = 4.301162634 Simplifying x + -4.5 = 4.301162634 Reorder the terms: -4.5 + x = 4.301162634 Solving -4.5 + x = 4.301162634 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 = 4.301162634 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.301162634 + 4.5 x = 4.301162634 + 4.5 Combine like terms: 4.301162634 + 4.5 = 8.801162634 x = 8.801162634 Simplifying x = 8.801162634

Subproblem 2

x + -4.5 = -4.301162634 Simplifying x + -4.5 = -4.301162634 Reorder the terms: -4.5 + x = -4.301162634 Solving -4.5 + x = -4.301162634 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 = -4.301162634 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.301162634 + 4.5 x = -4.301162634 + 4.5 Combine like terms: -4.301162634 + 4.5 = 0.198837366 x = 0.198837366 Simplifying x = 0.198837366

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.801162634, 0.198837366}

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