4*x^2-72*x+195=0

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Solution for 4*x^2-72*x+195=0 equation:


Simplifying
4x2 + -72x + 195 = 0

Reorder the terms:
195 + -72x + 4x2 = 0

Solving
195 + -72x + 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'.
48.75 + -18x + x2 = 0

Move the constant term to the right:

Add '-48.75' to each side of the equation.
48.75 + -18x + -48.75 + x2 = 0 + -48.75

Reorder the terms:
48.75 + -48.75 + -18x + x2 = 0 + -48.75

Combine like terms: 48.75 + -48.75 = 0.00
0.00 + -18x + x2 = 0 + -48.75
-18x + x2 = 0 + -48.75

Combine like terms: 0 + -48.75 = -48.75
-18x + x2 = -48.75

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -48.75 + 81

Reorder the terms:
81 + -18x + x2 = -48.75 + 81

Combine like terms: -48.75 + 81 = 32.25
81 + -18x + x2 = 32.25

Factor a perfect square on the left side:
(x + -9)(x + -9) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -9) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + -9 = 5.678908346 Simplifying x + -9 = 5.678908346 Reorder the terms: -9 + x = 5.678908346 Solving -9 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 5.678908346 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.678908346 + 9 x = 5.678908346 + 9 Combine like terms: 5.678908346 + 9 = 14.678908346 x = 14.678908346 Simplifying x = 14.678908346

Subproblem 2

x + -9 = -5.678908346 Simplifying x + -9 = -5.678908346 Reorder the terms: -9 + x = -5.678908346 Solving -9 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -5.678908346 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.678908346 + 9 x = -5.678908346 + 9 Combine like terms: -5.678908346 + 9 = 3.321091654 x = 3.321091654 Simplifying x = 3.321091654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.678908346, 3.321091654}

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