4x^2-74=x^2+1

Solution for 4x^2-74=x^2+1 equation:

Simplifying
4x2 + -74 = x2 + 1

Reorder the terms:
-74 + 4x2 = x2 + 1

Reorder the terms:
-74 + 4x2 = 1 + x2

Solving
-74 + 4x2 = 1 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
-74 + 4x2 + -1x2 = 1 + x2 + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-74 + 3x2 = 1 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-74 + 3x2 = 1 + 0
-74 + 3x2 = 1

Add '74' to each side of the equation.
-74 + 74 + 3x2 = 1 + 74

Combine like terms: -74 + 74 = 0
0 + 3x2 = 1 + 74
3x2 = 1 + 74

Combine like terms: 1 + 74 = 75
3x2 = 75

Divide each side by '3'.
x2 = 25

Simplifying
x2 = 25

Take the square root of each side:
x = {-5, 5}