(4x+3)(2x+7)=274

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Solution for (4x+3)(2x+7)=274 equation:


Simplifying
(4x + 3)(2x + 7) = 274

Reorder the terms:
(3 + 4x)(2x + 7) = 274

Reorder the terms:
(3 + 4x)(7 + 2x) = 274

Multiply (3 + 4x) * (7 + 2x)
(3(7 + 2x) + 4x * (7 + 2x)) = 274
((7 * 3 + 2x * 3) + 4x * (7 + 2x)) = 274
((21 + 6x) + 4x * (7 + 2x)) = 274
(21 + 6x + (7 * 4x + 2x * 4x)) = 274
(21 + 6x + (28x + 8x2)) = 274

Combine like terms: 6x + 28x = 34x
(21 + 34x + 8x2) = 274

Solving
21 + 34x + 8x2 = 274

Solving for variable 'x'.

Reorder the terms:
21 + -274 + 34x + 8x2 = 274 + -274

Combine like terms: 21 + -274 = -253
-253 + 34x + 8x2 = 274 + -274

Combine like terms: 274 + -274 = 0
-253 + 34x + 8x2 = 0

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

Divide each side by '8'.
-31.625 + 4.25x + x2 = 0

Move the constant term to the right:

Add '31.625' to each side of the equation.
-31.625 + 4.25x + 31.625 + x2 = 0 + 31.625

Reorder the terms:
-31.625 + 31.625 + 4.25x + x2 = 0 + 31.625

Combine like terms: -31.625 + 31.625 = 0.000
0.000 + 4.25x + x2 = 0 + 31.625
4.25x + x2 = 0 + 31.625

Combine like terms: 0 + 31.625 = 31.625
4.25x + x2 = 31.625

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 31.625 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 31.625 + 4.515625

Combine like terms: 31.625 + 4.515625 = 36.140625
4.515625 + 4.25x + x2 = 36.140625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 36.140625

Calculate the square root of the right side: 6.011707328

Break this problem into two subproblems by setting 
(x + 2.125) equal to 6.011707328 and -6.011707328.

Subproblem 1

x + 2.125 = 6.011707328 Simplifying x + 2.125 = 6.011707328 Reorder the terms: 2.125 + x = 6.011707328 Solving 2.125 + x = 6.011707328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 6.011707328 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 6.011707328 + -2.125 x = 6.011707328 + -2.125 Combine like terms: 6.011707328 + -2.125 = 3.886707328 x = 3.886707328 Simplifying x = 3.886707328

Subproblem 2

x + 2.125 = -6.011707328 Simplifying x + 2.125 = -6.011707328 Reorder the terms: 2.125 + x = -6.011707328 Solving 2.125 + x = -6.011707328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -6.011707328 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -6.011707328 + -2.125 x = -6.011707328 + -2.125 Combine like terms: -6.011707328 + -2.125 = -8.136707328 x = -8.136707328 Simplifying x = -8.136707328

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.886707328, -8.136707328}

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