16x^2+40x+25=7

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Solution for 16x^2+40x+25=7 equation: 


Simplifying
16x2 + 40x + 25 = 7

Reorder the terms:
25 + 40x + 16x2 = 7

Solving
25 + 40x + 16x2 = 7

Solving for variable 'x'.

Reorder the terms:
25 + -7 + 40x + 16x2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + 40x + 16x2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + 40x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 20x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 20x + 8x2)' equal to zero and attempt to solve:

Simplifying
9 + 20x + 8x2 = 0

Solving
9 + 20x + 8x2 = 0

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

Divide each side by '8'.
1.125 + 2.5x + x2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + 2.5x + -1.125 + x2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + 2.5x + x2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + 2.5x + x2 = 0 + -1.125
2.5x + x2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
2.5x + x2 = -1.125

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -1.125 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -1.125 + 1.5625

Combine like terms: -1.125 + 1.5625 = 0.4375
1.5625 + 2.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.661437828 and -0.661437828.


Subproblem 1
x + 1.25 = 0.661437828

Simplifying
x + 1.25 = 0.661437828

Reorder the terms:
1.25 + x = 0.661437828

Solving
1.25 + x = 0.661437828

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.661437828 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.661437828 + -1.25
x = 0.661437828 + -1.25

Combine like terms: 0.661437828 + -1.25 = -0.588562172
x = -0.588562172

Simplifying
x = -0.588562172


Subproblem 2
x + 1.25 = -0.661437828

Simplifying
x + 1.25 = -0.661437828

Reorder the terms:
1.25 + x = -0.661437828

Solving
1.25 + x = -0.661437828

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.661437828 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.661437828 + -1.25
x = -0.661437828 + -1.25

Combine like terms: -0.661437828 + -1.25 = -1.911437828
x = -1.911437828

Simplifying
x = -1.911437828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.588562172, -1.911437828}
Solution
x = {-0.588562172, -1.911437828}

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