7x-28+(4x+1)(2-1x)=0

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Solution for 7x-28+(4x+1)(2-1x)=0 equation:


Simplifying
7x + -28 + (4x + 1)(2 + -1x) = 0

Reorder the terms:
7x + -28 + (1 + 4x)(2 + -1x) = 0

Multiply (1 + 4x) * (2 + -1x)
7x + -28 + (1(2 + -1x) + 4x * (2 + -1x)) = 0
7x + -28 + ((2 * 1 + -1x * 1) + 4x * (2 + -1x)) = 0
7x + -28 + ((2 + -1x) + 4x * (2 + -1x)) = 0
7x + -28 + (2 + -1x + (2 * 4x + -1x * 4x)) = 0
7x + -28 + (2 + -1x + (8x + -4x2)) = 0

Combine like terms: -1x + 8x = 7x
7x + -28 + (2 + 7x + -4x2) = 0

Reorder the terms:
-28 + 2 + 7x + 7x + -4x2 = 0

Combine like terms: -28 + 2 = -26
-26 + 7x + 7x + -4x2 = 0

Combine like terms: 7x + 7x = 14x
-26 + 14x + -4x2 = 0

Solving
-26 + 14x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 7x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + 7x + -2x2)' equal to zero and attempt to solve: Simplifying -13 + 7x + -2x2 = 0 Solving -13 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -3.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -3.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -3.5x + x2 = 0 + -6.5 -3.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -3.5x + x2 = -6.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -6.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -6.5 + 3.0625 Combine like terms: -6.5 + 3.0625 = -3.4375 3.0625 + -3.5x + x2 = -3.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -3.4375 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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