(2x-7)*(x+4)=184

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Solution for (2x-7)*(x+4)=184 equation:


Simplifying
(2x + -7)(x + 4) = 184

Reorder the terms:
(-7 + 2x)(x + 4) = 184

Reorder the terms:
(-7 + 2x)(4 + x) = 184

Multiply (-7 + 2x) * (4 + x)
(-7(4 + x) + 2x * (4 + x)) = 184
((4 * -7 + x * -7) + 2x * (4 + x)) = 184
((-28 + -7x) + 2x * (4 + x)) = 184
(-28 + -7x + (4 * 2x + x * 2x)) = 184
(-28 + -7x + (8x + 2x2)) = 184

Combine like terms: -7x + 8x = 1x
(-28 + 1x + 2x2) = 184

Solving
-28 + 1x + 2x2 = 184

Solving for variable 'x'.

Reorder the terms:
-28 + -184 + 1x + 2x2 = 184 + -184

Combine like terms: -28 + -184 = -212
-212 + 1x + 2x2 = 184 + -184

Combine like terms: 184 + -184 = 0
-212 + 1x + 2x2 = 0

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

Divide each side by '2'.
-106 + 0.5x + x2 = 0

Move the constant term to the right:

Add '106' to each side of the equation.
-106 + 0.5x + 106 + x2 = 0 + 106

Reorder the terms:
-106 + 106 + 0.5x + x2 = 0 + 106

Combine like terms: -106 + 106 = 0
0 + 0.5x + x2 = 0 + 106
0.5x + x2 = 0 + 106

Combine like terms: 0 + 106 = 106
0.5x + x2 = 106

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 106 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 106 + 0.0625

Combine like terms: 106 + 0.0625 = 106.0625
0.0625 + 0.5x + x2 = 106.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 106.0625

Calculate the square root of the right side: 10.298664962

Break this problem into two subproblems by setting 
(x + 0.25) equal to 10.298664962 and -10.298664962.

Subproblem 1

x + 0.25 = 10.298664962 Simplifying x + 0.25 = 10.298664962 Reorder the terms: 0.25 + x = 10.298664962 Solving 0.25 + x = 10.298664962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 10.298664962 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 10.298664962 + -0.25 x = 10.298664962 + -0.25 Combine like terms: 10.298664962 + -0.25 = 10.048664962 x = 10.048664962 Simplifying x = 10.048664962

Subproblem 2

x + 0.25 = -10.298664962 Simplifying x + 0.25 = -10.298664962 Reorder the terms: 0.25 + x = -10.298664962 Solving 0.25 + x = -10.298664962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -10.298664962 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -10.298664962 + -0.25 x = -10.298664962 + -0.25 Combine like terms: -10.298664962 + -0.25 = -10.548664962 x = -10.548664962 Simplifying x = -10.548664962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.048664962, -10.548664962}

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