2x^2-80=x^2+6x+25

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Solution for 2x^2-80=x^2+6x+25 equation:


Simplifying
2x2 + -80 = x2 + 6x + 25

Reorder the terms:
-80 + 2x2 = x2 + 6x + 25

Reorder the terms:
-80 + 2x2 = 25 + 6x + x2

Solving
-80 + 2x2 = 25 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-80 + -25 + -6x + 2x2 + -1x2 = 25 + 6x + x2 + -25 + -6x + -1x2

Combine like terms: -80 + -25 = -105
-105 + -6x + 2x2 + -1x2 = 25 + 6x + x2 + -25 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-105 + -6x + 1x2 = 25 + 6x + x2 + -25 + -6x + -1x2

Reorder the terms:
-105 + -6x + 1x2 = 25 + -25 + 6x + -6x + x2 + -1x2

Combine like terms: 25 + -25 = 0
-105 + -6x + 1x2 = 0 + 6x + -6x + x2 + -1x2
-105 + -6x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-105 + -6x + 1x2 = 0 + x2 + -1x2
-105 + -6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-105 + -6x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -6x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + -6x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -6x + x2 = 0 + 105
-6x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
-6x + x2 = 105

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 105 + 9

Reorder the terms:
9 + -6x + x2 = 105 + 9

Combine like terms: 105 + 9 = 114
9 + -6x + x2 = 114

Factor a perfect square on the left side:
(x + -3)(x + -3) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + -3) equal to 10.677078252 and -10.677078252.

Subproblem 1

x + -3 = 10.677078252 Simplifying x + -3 = 10.677078252 Reorder the terms: -3 + x = 10.677078252 Solving -3 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 10.677078252 + 3 Combine like terms: -3 + 3 = 0 0 + x = 10.677078252 + 3 x = 10.677078252 + 3 Combine like terms: 10.677078252 + 3 = 13.677078252 x = 13.677078252 Simplifying x = 13.677078252

Subproblem 2

x + -3 = -10.677078252 Simplifying x + -3 = -10.677078252 Reorder the terms: -3 + x = -10.677078252 Solving -3 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -10.677078252 + 3 Combine like terms: -3 + 3 = 0 0 + x = -10.677078252 + 3 x = -10.677078252 + 3 Combine like terms: -10.677078252 + 3 = -7.677078252 x = -7.677078252 Simplifying x = -7.677078252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.677078252, -7.677078252}

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