5x(2x-7)+(-8)=16

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Solution for 5x(2x-7)+(-8)=16 equation:


Simplifying
5x(2x + -7) + (-8) = 16

Reorder the terms:
5x(-7 + 2x) + (-8) = 16
(-7 * 5x + 2x * 5x) + (-8) = 16
(-35x + 10x2) + (-8) = 16
-35x + 10x2 + -8 = 16

Reorder the terms:
-8 + -35x + 10x2 = 16

Solving
-8 + -35x + 10x2 = 16

Solving for variable 'x'.

Reorder the terms:
-8 + -16 + -35x + 10x2 = 16 + -16

Combine like terms: -8 + -16 = -24
-24 + -35x + 10x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-24 + -35x + 10x2 = 0

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

Divide each side by '10'.
-2.4 + -3.5x + x2 = 0.0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -3.5x + 2.4 + x2 = 0.0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -3.5x + x2 = 0.0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -3.5x + x2 = 0.0 + 2.4
-3.5x + x2 = 0.0 + 2.4

Combine like terms: 0.0 + 2.4 = 2.4
-3.5x + x2 = 2.4

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 = 2.4 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 2.4 + 3.0625

Combine like terms: 2.4 + 3.0625 = 5.4625
3.0625 + -3.5x + x2 = 5.4625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 5.4625

Calculate the square root of the right side: 2.337199179

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.337199179 and -2.337199179.


Subproblem 1
x + -1.75 = 2.337199179

Simplifying
x + -1.75 = 2.337199179

Reorder the terms:
-1.75 + x = 2.337199179

Solving
-1.75 + x = 2.337199179

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.337199179 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.337199179 + 1.75
x = 2.337199179 + 1.75

Combine like terms: 2.337199179 + 1.75 = 4.087199179
x = 4.087199179

Simplifying
x = 4.087199179


Subproblem 2
x + -1.75 = -2.337199179

Simplifying
x + -1.75 = -2.337199179

Reorder the terms:
-1.75 + x = -2.337199179

Solving
-1.75 + x = -2.337199179

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.337199179 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.337199179 + 1.75
x = -2.337199179 + 1.75

Combine like terms: -2.337199179 + 1.75 = -0.587199179
x = -0.587199179

Simplifying
x = -0.587199179


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.087199179, -0.587199179}

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