2x^2-25x=3x^2+60

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Solution for 2x^2-25x=3x^2+60 equation: 


Simplifying
2x2 + -25x = 3x2 + 60

Reorder the terms:
-25x + 2x2 = 3x2 + 60

Reorder the terms:
-25x + 2x2 = 60 + 3x2

Solving
-25x + 2x2 = 60 + 3x2

Solving for variable 'x'.

Reorder the terms:
-60 + -25x + 2x2 + -3x2 = 60 + 3x2 + -60 + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-60 + -25x + -1x2 = 60 + 3x2 + -60 + -3x2

Reorder the terms:
-60 + -25x + -1x2 = 60 + -60 + 3x2 + -3x2

Combine like terms: 60 + -60 = 0
-60 + -25x + -1x2 = 0 + 3x2 + -3x2
-60 + -25x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-60 + -25x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(60 + 25x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(60 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
60 + 25x + x2 = 0

Solving
60 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 25x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 25x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 25x + x2 = 0 + -60
25x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
25x + x2 = -60

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -60 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -60 + 156.25

Combine like terms: -60 + 156.25 = 96.25
156.25 + 25x + x2 = 96.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 12.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + 12.5 = 9.810708435

Simplifying
x + 12.5 = 9.810708435

Reorder the terms:
12.5 + x = 9.810708435

Solving
12.5 + x = 9.810708435

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 9.810708435 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 9.810708435 + -12.5
x = 9.810708435 + -12.5

Combine like terms: 9.810708435 + -12.5 = -2.689291565
x = -2.689291565

Simplifying
x = -2.689291565


Subproblem 2
x + 12.5 = -9.810708435

Simplifying
x + 12.5 = -9.810708435

Reorder the terms:
12.5 + x = -9.810708435

Solving
12.5 + x = -9.810708435

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -9.810708435 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -9.810708435 + -12.5
x = -9.810708435 + -12.5

Combine like terms: -9.810708435 + -12.5 = -22.310708435
x = -22.310708435

Simplifying
x = -22.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.689291565, -22.310708435}
Solution
x = {-2.689291565, -22.310708435}

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