2x(2x+1)=7x-4

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Solution for 2x(2x+1)=7x-4 equation: 


Simplifying
2x(2x + 1) = 7x + -4

Reorder the terms:
2x(1 + 2x) = 7x + -4
(1 * 2x + 2x * 2x) = 7x + -4
(2x + 4x2) = 7x + -4

Reorder the terms:
2x + 4x2 = -4 + 7x

Solving
2x + 4x2 = -4 + 7x

Solving for variable 'x'.

Reorder the terms:
4 + 2x + -7x + 4x2 = -4 + 7x + 4 + -7x

Combine like terms: 2x + -7x = -5x
4 + -5x + 4x2 = -4 + 7x + 4 + -7x

Reorder the terms:
4 + -5x + 4x2 = -4 + 4 + 7x + -7x

Combine like terms: -4 + 4 = 0
4 + -5x + 4x2 = 0 + 7x + -7x
4 + -5x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
4 + -5x + 4x2 = 0

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

Divide each side by '4'.
1 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.25x + x2 = 0 + -1
-1.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.25x + x2 = -1

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -1 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -1 + 0.390625

Combine like terms: -1 + 0.390625 = -0.609375
0.390625 + -1.25x + x2 = -0.609375

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = -0.609375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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