4x(x+7)-4=18+5x

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Solution for 4x(x+7)-4=18+5x equation:


Simplifying
4x(x + 7) + -4 = 18 + 5x

Reorder the terms:
4x(7 + x) + -4 = 18 + 5x
(7 * 4x + x * 4x) + -4 = 18 + 5x
(28x + 4x2) + -4 = 18 + 5x

Reorder the terms:
-4 + 28x + 4x2 = 18 + 5x

Solving
-4 + 28x + 4x2 = 18 + 5x

Solving for variable 'x'.

Reorder the terms:
-4 + -18 + 28x + -5x + 4x2 = 18 + 5x + -18 + -5x

Combine like terms: -4 + -18 = -22
-22 + 28x + -5x + 4x2 = 18 + 5x + -18 + -5x

Combine like terms: 28x + -5x = 23x
-22 + 23x + 4x2 = 18 + 5x + -18 + -5x

Reorder the terms:
-22 + 23x + 4x2 = 18 + -18 + 5x + -5x

Combine like terms: 18 + -18 = 0
-22 + 23x + 4x2 = 0 + 5x + -5x
-22 + 23x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-22 + 23x + 4x2 = 0

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

Divide each side by '4'.
-5.5 + 5.75x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 5.75x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 5.75x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 5.75x + x2 = 0 + 5.5
5.75x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
5.75x + x2 = 5.5

The x term is 5.75x.  Take half its coefficient (2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
5.75x + 8.265625 + x2 = 5.5 + 8.265625

Reorder the terms:
8.265625 + 5.75x + x2 = 5.5 + 8.265625

Combine like terms: 5.5 + 8.265625 = 13.765625
8.265625 + 5.75x + x2 = 13.765625

Factor a perfect square on the left side:
(x + 2.875)(x + 2.875) = 13.765625

Calculate the square root of the right side: 3.71020552

Break this problem into two subproblems by setting 
(x + 2.875) equal to 3.71020552 and -3.71020552.

Subproblem 1

x + 2.875 = 3.71020552 Simplifying x + 2.875 = 3.71020552 Reorder the terms: 2.875 + x = 3.71020552 Solving 2.875 + x = 3.71020552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 3.71020552 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 3.71020552 + -2.875 x = 3.71020552 + -2.875 Combine like terms: 3.71020552 + -2.875 = 0.83520552 x = 0.83520552 Simplifying x = 0.83520552

Subproblem 2

x + 2.875 = -3.71020552 Simplifying x + 2.875 = -3.71020552 Reorder the terms: 2.875 + x = -3.71020552 Solving 2.875 + x = -3.71020552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -3.71020552 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -3.71020552 + -2.875 x = -3.71020552 + -2.875 Combine like terms: -3.71020552 + -2.875 = -6.58520552 x = -6.58520552 Simplifying x = -6.58520552

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.83520552, -6.58520552}

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