(3x^2+10)=(9x+50)

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Solution for (3x^2+10)=(9x+50) equation:


Simplifying
(3x2 + 10) = (9x + 50)

Reorder the terms:
(10 + 3x2) = (9x + 50)

Remove parenthesis around (10 + 3x2)
10 + 3x2 = (9x + 50)

Reorder the terms:
10 + 3x2 = (50 + 9x)

Remove parenthesis around (50 + 9x)
10 + 3x2 = 50 + 9x

Solving
10 + 3x2 = 50 + 9x

Solving for variable 'x'.

Reorder the terms:
10 + -50 + -9x + 3x2 = 50 + 9x + -50 + -9x

Combine like terms: 10 + -50 = -40
-40 + -9x + 3x2 = 50 + 9x + -50 + -9x

Reorder the terms:
-40 + -9x + 3x2 = 50 + -50 + 9x + -9x

Combine like terms: 50 + -50 = 0
-40 + -9x + 3x2 = 0 + 9x + -9x
-40 + -9x + 3x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-40 + -9x + 3x2 = 0

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

Divide each side by '3'.
-13.33333333 + -3x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -3x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -3x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -3x + x2 = 0 + 13.33333333
-3x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-3x + x2 = 13.33333333

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 = 13.33333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 13.33333333 + 2.25

Combine like terms: 13.33333333 + 2.25 = 15.58333333
2.25 + -3x + x2 = 15.58333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 15.58333333

Calculate the square root of the right side: 3.947573094

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.947573094 and -3.947573094.

Subproblem 1

x + -1.5 = 3.947573094 Simplifying x + -1.5 = 3.947573094 Reorder the terms: -1.5 + x = 3.947573094 Solving -1.5 + x = 3.947573094 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 = 3.947573094 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.947573094 + 1.5 x = 3.947573094 + 1.5 Combine like terms: 3.947573094 + 1.5 = 5.447573094 x = 5.447573094 Simplifying x = 5.447573094

Subproblem 2

x + -1.5 = -3.947573094 Simplifying x + -1.5 = -3.947573094 Reorder the terms: -1.5 + x = -3.947573094 Solving -1.5 + x = -3.947573094 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 = -3.947573094 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.947573094 + 1.5 x = -3.947573094 + 1.5 Combine like terms: -3.947573094 + 1.5 = -2.447573094 x = -2.447573094 Simplifying x = -2.447573094

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.447573094, -2.447573094}

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