8x^2-28x+19=0

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Solution for 8x^2-28x+19=0 equation:


Simplifying
8x2 + -28x + 19 = 0

Reorder the terms:
19 + -28x + 8x2 = 0

Solving
19 + -28x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
2.375 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-2.375' to each side of the equation.
2.375 + -3.5x + -2.375 + x2 = 0 + -2.375

Reorder the terms:
2.375 + -2.375 + -3.5x + x2 = 0 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + -3.5x + x2 = 0 + -2.375
-3.5x + x2 = 0 + -2.375

Combine like terms: 0 + -2.375 = -2.375
-3.5x + x2 = -2.375

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2.375 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2.375 + 3.0625

Combine like terms: -2.375 + 3.0625 = 0.6875
3.0625 + -3.5x + x2 = 0.6875

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(x + -1.75) equal to 0.829156198 and -0.829156198.

Subproblem 1

x + -1.75 = 0.829156198 Simplifying x + -1.75 = 0.829156198 Reorder the terms: -1.75 + x = 0.829156198 Solving -1.75 + x = 0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 0.829156198 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.829156198 + 1.75 x = 0.829156198 + 1.75 Combine like terms: 0.829156198 + 1.75 = 2.579156198 x = 2.579156198 Simplifying x = 2.579156198

Subproblem 2

x + -1.75 = -0.829156198 Simplifying x + -1.75 = -0.829156198 Reorder the terms: -1.75 + x = -0.829156198 Solving -1.75 + x = -0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -0.829156198 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -0.829156198 + 1.75 x = -0.829156198 + 1.75 Combine like terms: -0.829156198 + 1.75 = 0.920843802 x = 0.920843802 Simplifying x = 0.920843802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.579156198, 0.920843802}

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