2x^2+31=5x+7

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Solution for 2x^2+31=5x+7 equation: 


Simplifying
2x2 + 31 = 5x + 7

Reorder the terms:
31 + 2x2 = 5x + 7

Reorder the terms:
31 + 2x2 = 7 + 5x

Solving
31 + 2x2 = 7 + 5x

Solving for variable 'x'.

Reorder the terms:
31 + -7 + -5x + 2x2 = 7 + 5x + -7 + -5x

Combine like terms: 31 + -7 = 24
24 + -5x + 2x2 = 7 + 5x + -7 + -5x

Reorder the terms:
24 + -5x + 2x2 = 7 + -7 + 5x + -5x

Combine like terms: 7 + -7 = 0
24 + -5x + 2x2 = 0 + 5x + -5x
24 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
24 + -5x + 2x2 = 0

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

Divide each side by '2'.
12 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -2.5x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -2.5x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -2.5x + x2 = 0 + -12
-2.5x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-2.5x + x2 = -12

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -12 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -12 + 1.5625

Combine like terms: -12 + 1.5625 = -10.4375
1.5625 + -2.5x + x2 = -10.4375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = -10.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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