3x^2-9x=7

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


Simplifying
3x2 + -9x = 7

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

Solving
-9x + 3x2 = 7

Solving for variable 'x'.

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

Combine like terms: 7 + -7 = 0
-7 + -9x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -3x + x2 = 0

Move the constant term to the right:

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

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

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 2.333333333
-3x + x2 = 0 + 2.333333333

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.333333333 + 2.25

Combine like terms: 2.333333333 + 2.25 = 4.583333333
2.25 + -3x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.140872096 and -2.140872096.

Subproblem 1

x + -1.5 = 2.140872096 Simplifying x + -1.5 = 2.140872096 Reorder the terms: -1.5 + x = 2.140872096 Solving -1.5 + x = 2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.140872096 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.140872096 + 1.5 x = 2.140872096 + 1.5 Combine like terms: 2.140872096 + 1.5 = 3.640872096 x = 3.640872096 Simplifying x = 3.640872096

Subproblem 2

x + -1.5 = -2.140872096 Simplifying x + -1.5 = -2.140872096 Reorder the terms: -1.5 + x = -2.140872096 Solving -1.5 + x = -2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.140872096 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.140872096 + 1.5 x = -2.140872096 + 1.5 Combine like terms: -2.140872096 + 1.5 = -0.640872096 x = -0.640872096 Simplifying x = -0.640872096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.640872096, -0.640872096}

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