3x^2+5+x=70

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Solution for 3x^2+5+x=70 equation:


Simplifying
3x2 + 5 + x = 70

Reorder the terms:
5 + x + 3x2 = 70

Solving
5 + x + 3x2 = 70

Solving for variable 'x'.

Reorder the terms:
5 + -70 + x + 3x2 = 70 + -70

Combine like terms: 5 + -70 = -65
-65 + x + 3x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-65 + x + 3x2 = 0

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

Divide each side by '3'.
-21.66666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '21.66666667' to each side of the equation.
-21.66666667 + 0.3333333333x + 21.66666667 + x2 = 0 + 21.66666667

Reorder the terms:
-21.66666667 + 21.66666667 + 0.3333333333x + x2 = 0 + 21.66666667

Combine like terms: -21.66666667 + 21.66666667 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 21.66666667
0.3333333333x + x2 = 0 + 21.66666667

Combine like terms: 0 + 21.66666667 = 21.66666667
0.3333333333x + x2 = 21.66666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 21.66666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 21.66666667 + 0.25

Combine like terms: 21.66666667 + 0.25 = 21.91666667
0.25 + 0.3333333333x + x2 = 21.91666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 21.91666667

Calculate the square root of the right side: 4.681523969

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.681523969 and -4.681523969.

Subproblem 1

x + 0.5 = 4.681523969 Simplifying x + 0.5 = 4.681523969 Reorder the terms: 0.5 + x = 4.681523969 Solving 0.5 + x = 4.681523969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.681523969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.681523969 + -0.5 x = 4.681523969 + -0.5 Combine like terms: 4.681523969 + -0.5 = 4.181523969 x = 4.181523969 Simplifying x = 4.181523969

Subproblem 2

x + 0.5 = -4.681523969 Simplifying x + 0.5 = -4.681523969 Reorder the terms: 0.5 + x = -4.681523969 Solving 0.5 + x = -4.681523969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.681523969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.681523969 + -0.5 x = -4.681523969 + -0.5 Combine like terms: -4.681523969 + -0.5 = -5.181523969 x = -5.181523969 Simplifying x = -5.181523969

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.181523969, -5.181523969}

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