3x^2-10x+8=8x+19

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Solution for 3x^2-10x+8=8x+19 equation:


Simplifying
3x2 + -10x + 8 = 8x + 19

Reorder the terms:
8 + -10x + 3x2 = 8x + 19

Reorder the terms:
8 + -10x + 3x2 = 19 + 8x

Solving
8 + -10x + 3x2 = 19 + 8x

Solving for variable 'x'.

Reorder the terms:
8 + -19 + -10x + -8x + 3x2 = 19 + 8x + -19 + -8x

Combine like terms: 8 + -19 = -11
-11 + -10x + -8x + 3x2 = 19 + 8x + -19 + -8x

Combine like terms: -10x + -8x = -18x
-11 + -18x + 3x2 = 19 + 8x + -19 + -8x

Reorder the terms:
-11 + -18x + 3x2 = 19 + -19 + 8x + -8x

Combine like terms: 19 + -19 = 0
-11 + -18x + 3x2 = 0 + 8x + -8x
-11 + -18x + 3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-11 + -18x + 3x2 = 0

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

Divide each side by '3'.
-3.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '3.666666667' to each side of the equation.
-3.666666667 + -6x + 3.666666667 + x2 = 0 + 3.666666667

Reorder the terms:
-3.666666667 + 3.666666667 + -6x + x2 = 0 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + 3.666666667
-6x + x2 = 0 + 3.666666667

Combine like terms: 0 + 3.666666667 = 3.666666667
-6x + x2 = 3.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 3.666666667 + 9

Reorder the terms:
9 + -6x + x2 = 3.666666667 + 9

Combine like terms: 3.666666667 + 9 = 12.666666667
9 + -6x + x2 = 12.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 12.666666667

Calculate the square root of the right side: 3.559026084

Break this problem into two subproblems by setting 
(x + -3) equal to 3.559026084 and -3.559026084.

Subproblem 1

x + -3 = 3.559026084 Simplifying x + -3 = 3.559026084 Reorder the terms: -3 + x = 3.559026084 Solving -3 + x = 3.559026084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.559026084 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.559026084 + 3 x = 3.559026084 + 3 Combine like terms: 3.559026084 + 3 = 6.559026084 x = 6.559026084 Simplifying x = 6.559026084

Subproblem 2

x + -3 = -3.559026084 Simplifying x + -3 = -3.559026084 Reorder the terms: -3 + x = -3.559026084 Solving -3 + x = -3.559026084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.559026084 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.559026084 + 3 x = -3.559026084 + 3 Combine like terms: -3.559026084 + 3 = -0.559026084 x = -0.559026084 Simplifying x = -0.559026084

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.559026084, -0.559026084}

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