4x^2+11x=3x-10

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Solution for 4x^2+11x=3x-10 equation: 


Simplifying
4x2 + 11x = 3x + -10

Reorder the terms:
11x + 4x2 = 3x + -10

Reorder the terms:
11x + 4x2 = -10 + 3x

Solving
11x + 4x2 = -10 + 3x

Solving for variable 'x'.

Reorder the terms:
10 + 11x + -3x + 4x2 = -10 + 3x + 10 + -3x

Combine like terms: 11x + -3x = 8x
10 + 8x + 4x2 = -10 + 3x + 10 + -3x

Reorder the terms:
10 + 8x + 4x2 = -10 + 10 + 3x + -3x

Combine like terms: -10 + 10 = 0
10 + 8x + 4x2 = 0 + 3x + -3x
10 + 8x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
10 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x + 2x2 = 0

Solving
5 + 4x + 2x2 = 0

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

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

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 2x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 2x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 2x + x2 = 0 + -2.5
2x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
2x + x2 = -2.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -2.5 + 1

Reorder the terms:
1 + 2x + x2 = -2.5 + 1

Combine like terms: -2.5 + 1 = -1.5
1 + 2x + x2 = -1.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -1.5

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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