4x^2-25x+19=-5+10

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Solution for 4x^2-25x+19=-5+10 equation: 


Simplifying
4x2 + -25x + 19 = -5 + 10

Reorder the terms:
19 + -25x + 4x2 = -5 + 10

Combine like terms: -5 + 10 = 5
19 + -25x + 4x2 = 5

Solving
19 + -25x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
19 + -5 + -25x + 4x2 = 5 + -5

Combine like terms: 19 + -5 = 14
14 + -25x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
14 + -25x + 4x2 = 0

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

Divide each side by '4'.
3.5 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -6.25x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -6.25x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -6.25x + x2 = 0 + -3.5
-6.25x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-6.25x + x2 = -3.5

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 = -3.5 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -3.5 + 9.765625

Combine like terms: -3.5 + 9.765625 = 6.265625
9.765625 + -6.25x + x2 = 6.265625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 6.265625

Calculate the square root of the right side: 2.503123049

Break this problem into two subproblems by setting 
(x + -3.125) equal to 2.503123049 and -2.503123049.


Subproblem 1
x + -3.125 = 2.503123049

Simplifying
x + -3.125 = 2.503123049

Reorder the terms:
-3.125 + x = 2.503123049

Solving
-3.125 + x = 2.503123049

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 = 2.503123049 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 2.503123049 + 3.125
x = 2.503123049 + 3.125

Combine like terms: 2.503123049 + 3.125 = 5.628123049
x = 5.628123049

Simplifying
x = 5.628123049


Subproblem 2
x + -3.125 = -2.503123049

Simplifying
x + -3.125 = -2.503123049

Reorder the terms:
-3.125 + x = -2.503123049

Solving
-3.125 + x = -2.503123049

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 = -2.503123049 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -2.503123049 + 3.125
x = -2.503123049 + 3.125

Combine like terms: -2.503123049 + 3.125 = 0.621876951
x = 0.621876951

Simplifying
x = 0.621876951


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.628123049, 0.621876951}

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