4x^2-36x+38.75=0

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Solution for 4x^2-36x+38.75=0 equation:


Simplifying
4x2 + -36x + 38.75 = 0

Reorder the terms:
38.75 + -36x + 4x2 = 0

Solving
38.75 + -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'.
9.6875 + -9x + x2 = 0

Move the constant term to the right:

Add '-9.6875' to each side of the equation.
9.6875 + -9x + -9.6875 + x2 = 0 + -9.6875

Reorder the terms:
9.6875 + -9.6875 + -9x + x2 = 0 + -9.6875

Combine like terms: 9.6875 + -9.6875 = 0.0000
0.0000 + -9x + x2 = 0 + -9.6875
-9x + x2 = 0 + -9.6875

Combine like terms: 0 + -9.6875 = -9.6875
-9x + x2 = -9.6875

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 = -9.6875 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -9.6875 + 20.25

Combine like terms: -9.6875 + 20.25 = 10.5625
20.25 + -9x + x2 = 10.5625

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.25 and -3.25.

Subproblem 1

x + -4.5 = 3.25 Simplifying x + -4.5 = 3.25 Reorder the terms: -4.5 + x = 3.25 Solving -4.5 + x = 3.25 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 = 3.25 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.25 + 4.5 x = 3.25 + 4.5 Combine like terms: 3.25 + 4.5 = 7.75 x = 7.75 Simplifying x = 7.75

Subproblem 2

x + -4.5 = -3.25 Simplifying x + -4.5 = -3.25 Reorder the terms: -4.5 + x = -3.25 Solving -4.5 + x = -3.25 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 = -3.25 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.25 + 4.5 x = -3.25 + 4.5 Combine like terms: -3.25 + 4.5 = 1.25 x = 1.25 Simplifying x = 1.25

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.75, 1.25}

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