=4x^2+x+10

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Solution for =4x^2+x+10 equation: 


Simplifying
0 = 4x2 + x + 10

Reorder the terms:
0 = 10 + x + 4x2

Solving
0 = 10 + x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -10 = -10
-10 + -1x + -4x2 = 10 + x + 4x2 + -10 + -1x + -4x2

Reorder the terms:
-10 + -1x + -4x2 = 10 + -10 + x + -1x + 4x2 + -4x2

Combine like terms: 10 + -10 = 0
-10 + -1x + -4x2 = 0 + x + -1x + 4x2 + -4x2
-10 + -1x + -4x2 = x + -1x + 4x2 + -4x2

Combine like terms: x + -1x = 0
-10 + -1x + -4x2 = 0 + 4x2 + -4x2
-10 + -1x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-10 + -1x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
10 + x + 4x2 = 0

Solving
10 + x + 4x2 = 0

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

Divide each side by '4'.
2.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 0.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 0.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 0.25x + x2 = 0 + -2.5
0.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
0.25x + x2 = -2.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = -2.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + 0.25x + x2 = -2.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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