3x^2-19x-15=0

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Solution for 3x^2-19x-15=0 equation:


Simplifying
3x2 + -19x + -15 = 0

Reorder the terms:
-15 + -19x + 3x2 = 0

Solving
-15 + -19x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-5 + -6.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -6.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6.333333333x + x2 = 0 + 5
-6.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6.333333333x + x2 = 5

The x term is -6.333333333x.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333x + 10.02777778 + x2 = 5 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333x + x2 = 5 + 10.02777778

Combine like terms: 5 + 10.02777778 = 15.02777778
10.02777778 + -6.333333333x + x2 = 15.02777778

Factor a perfect square on the left side:
(x + -3.166666667)(x + -3.166666667) = 15.02777778

Calculate the square root of the right side: 3.876567783

Break this problem into two subproblems by setting 
(x + -3.166666667) equal to 3.876567783 and -3.876567783.

Subproblem 1

x + -3.166666667 = 3.876567783 Simplifying x + -3.166666667 = 3.876567783 Reorder the terms: -3.166666667 + x = 3.876567783 Solving -3.166666667 + x = 3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 3.876567783 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 3.876567783 + 3.166666667 x = 3.876567783 + 3.166666667 Combine like terms: 3.876567783 + 3.166666667 = 7.04323445 x = 7.04323445 Simplifying x = 7.04323445

Subproblem 2

x + -3.166666667 = -3.876567783 Simplifying x + -3.166666667 = -3.876567783 Reorder the terms: -3.166666667 + x = -3.876567783 Solving -3.166666667 + x = -3.876567783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -3.876567783 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -3.876567783 + 3.166666667 x = -3.876567783 + 3.166666667 Combine like terms: -3.876567783 + 3.166666667 = -0.709901116 x = -0.709901116 Simplifying x = -0.709901116

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.04323445, -0.709901116}

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