3x^2-7x-9=0

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Solution for 3x^2-7x-9=0 equation:


Simplifying
3x2 + -7x + -9 = 0

Reorder the terms:
-9 + -7x + 3x2 = 0

Solving
-9 + -7x + 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'.
-3 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2.333333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -2.333333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2.333333333x + x2 = 0 + 3
-2.333333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2.333333333x + x2 = 3

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 3 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 3 + 1.361111112

Combine like terms: 3 + 1.361111112 = 4.361111112
1.361111112 + -2.333333333x + x2 = 4.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 4.361111112

Calculate the square root of the right side: 2.088327348

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.088327348 and -2.088327348.

Subproblem 1

x + -1.166666667 = 2.088327348 Simplifying x + -1.166666667 = 2.088327348 Reorder the terms: -1.166666667 + x = 2.088327348 Solving -1.166666667 + x = 2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 2.088327348 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 2.088327348 + 1.166666667 x = 2.088327348 + 1.166666667 Combine like terms: 2.088327348 + 1.166666667 = 3.254994015 x = 3.254994015 Simplifying x = 3.254994015

Subproblem 2

x + -1.166666667 = -2.088327348 Simplifying x + -1.166666667 = -2.088327348 Reorder the terms: -1.166666667 + x = -2.088327348 Solving -1.166666667 + x = -2.088327348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -2.088327348 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -2.088327348 + 1.166666667 x = -2.088327348 + 1.166666667 Combine like terms: -2.088327348 + 1.166666667 = -0.921660681 x = -0.921660681 Simplifying x = -0.921660681

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.254994015, -0.921660681}

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