5x^2-19x+3=0

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Solution for 5x^2-19x+3=0 equation:


Simplifying
5x2 + -19x + 3 = 0

Reorder the terms:
3 + -19x + 5x2 = 0

Solving
3 + -19x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.6 + -3.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -3.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -3.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -3.8x + x2 = 0 + -0.6
-3.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-3.8x + x2 = -0.6

The x term is -3.8x.  Take half its coefficient (-1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
-3.8x + 3.61 + x2 = -0.6 + 3.61

Reorder the terms:
3.61 + -3.8x + x2 = -0.6 + 3.61

Combine like terms: -0.6 + 3.61 = 3.01
3.61 + -3.8x + x2 = 3.01

Factor a perfect square on the left side:
(x + -1.9)(x + -1.9) = 3.01

Calculate the square root of the right side: 1.734935157

Break this problem into two subproblems by setting 
(x + -1.9) equal to 1.734935157 and -1.734935157.

Subproblem 1

x + -1.9 = 1.734935157 Simplifying x + -1.9 = 1.734935157 Reorder the terms: -1.9 + x = 1.734935157 Solving -1.9 + x = 1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 1.734935157 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 1.734935157 + 1.9 x = 1.734935157 + 1.9 Combine like terms: 1.734935157 + 1.9 = 3.634935157 x = 3.634935157 Simplifying x = 3.634935157

Subproblem 2

x + -1.9 = -1.734935157 Simplifying x + -1.9 = -1.734935157 Reorder the terms: -1.9 + x = -1.734935157 Solving -1.9 + x = -1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -1.734935157 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -1.734935157 + 1.9 x = -1.734935157 + 1.9 Combine like terms: -1.734935157 + 1.9 = 0.165064843 x = 0.165064843 Simplifying x = 0.165064843

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.634935157, 0.165064843}

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