3x^2=9x+10

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Solution for 3x^2=9x+10 equation:


Simplifying
3x2 = 9x + 10

Reorder the terms:
3x2 = 10 + 9x

Solving
3x2 = 10 + 9x

Solving for variable 'x'.

Reorder the terms:
-10 + -9x + 3x2 = 10 + 9x + -10 + -9x

Reorder the terms:
-10 + -9x + 3x2 = 10 + -10 + 9x + -9x

Combine like terms: 10 + -10 = 0
-10 + -9x + 3x2 = 0 + 9x + -9x
-10 + -9x + 3x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-10 + -9x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -3x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -3x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 3.333333333
-3x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-3x + x2 = 3.333333333

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 = 3.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 3.333333333 + 2.25

Combine like terms: 3.333333333 + 2.25 = 5.583333333
2.25 + -3x + x2 = 5.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 5.583333333

Calculate the square root of the right side: 2.362907813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.362907813 and -2.362907813.

Subproblem 1

x + -1.5 = 2.362907813 Simplifying x + -1.5 = 2.362907813 Reorder the terms: -1.5 + x = 2.362907813 Solving -1.5 + x = 2.362907813 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 = 2.362907813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.362907813 + 1.5 x = 2.362907813 + 1.5 Combine like terms: 2.362907813 + 1.5 = 3.862907813 x = 3.862907813 Simplifying x = 3.862907813

Subproblem 2

x + -1.5 = -2.362907813 Simplifying x + -1.5 = -2.362907813 Reorder the terms: -1.5 + x = -2.362907813 Solving -1.5 + x = -2.362907813 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 = -2.362907813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.362907813 + 1.5 x = -2.362907813 + 1.5 Combine like terms: -2.362907813 + 1.5 = -0.862907813 x = -0.862907813 Simplifying x = -0.862907813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.862907813, -0.862907813}

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