3x^2+5=30x+25

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Solution for 3x^2+5=30x+25 equation:


Simplifying
3x2 + 5 = 30x + 25

Reorder the terms:
5 + 3x2 = 30x + 25

Reorder the terms:
5 + 3x2 = 25 + 30x

Solving
5 + 3x2 = 25 + 30x

Solving for variable 'x'.

Reorder the terms:
5 + -25 + -30x + 3x2 = 25 + 30x + -25 + -30x

Combine like terms: 5 + -25 = -20
-20 + -30x + 3x2 = 25 + 30x + -25 + -30x

Reorder the terms:
-20 + -30x + 3x2 = 25 + -25 + 30x + -30x

Combine like terms: 25 + -25 = 0
-20 + -30x + 3x2 = 0 + 30x + -30x
-20 + -30x + 3x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-20 + -30x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + -10x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -10x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -10x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -10x + x2 = 0 + 6.666666667
-10x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-10x + x2 = 6.666666667

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 6.666666667 + 25

Reorder the terms:
25 + -10x + x2 = 6.666666667 + 25

Combine like terms: 6.666666667 + 25 = 31.666666667
25 + -10x + x2 = 31.666666667

Factor a perfect square on the left side:
(x + -5)(x + -5) = 31.666666667

Calculate the square root of the right side: 5.627314339

Break this problem into two subproblems by setting 
(x + -5) equal to 5.627314339 and -5.627314339.

Subproblem 1

x + -5 = 5.627314339 Simplifying x + -5 = 5.627314339 Reorder the terms: -5 + x = 5.627314339 Solving -5 + x = 5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.627314339 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.627314339 + 5 x = 5.627314339 + 5 Combine like terms: 5.627314339 + 5 = 10.627314339 x = 10.627314339 Simplifying x = 10.627314339

Subproblem 2

x + -5 = -5.627314339 Simplifying x + -5 = -5.627314339 Reorder the terms: -5 + x = -5.627314339 Solving -5 + x = -5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.627314339 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.627314339 + 5 x = -5.627314339 + 5 Combine like terms: -5.627314339 + 5 = -0.627314339 x = -0.627314339 Simplifying x = -0.627314339

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.627314339, -0.627314339}

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