4x^2-25x+38=0

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Solution for 4x^2-25x+38=0 equation:


Simplifying
4x2 + -25x + 38 = 0

Reorder the terms:
38 + -25x + 4x2 = 0

Solving
38 + -25x + 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'.
9.5 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + -6.25x + -9.5 + x2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + -6.25x + x2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + -6.25x + x2 = 0 + -9.5
-6.25x + x2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
-6.25x + x2 = -9.5

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -9.5 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -9.5 + 9.765625

Combine like terms: -9.5 + 9.765625 = 0.265625
9.765625 + -6.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + -3.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

x + -3.125 = 0.515388203 Simplifying x + -3.125 = 0.515388203 Reorder the terms: -3.125 + x = 0.515388203 Solving -3.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 0.515388203 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 0.515388203 + 3.125 x = 0.515388203 + 3.125 Combine like terms: 0.515388203 + 3.125 = 3.640388203 x = 3.640388203 Simplifying x = 3.640388203

Subproblem 2

x + -3.125 = -0.515388203 Simplifying x + -3.125 = -0.515388203 Reorder the terms: -3.125 + x = -0.515388203 Solving -3.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -0.515388203 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -0.515388203 + 3.125 x = -0.515388203 + 3.125 Combine like terms: -0.515388203 + 3.125 = 2.609611797 x = 2.609611797 Simplifying x = 2.609611797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.640388203, 2.609611797}

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