4(x^2+7x+12)=100

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Solution for 4(x^2+7x+12)=100 equation: 


Simplifying
4(x2 + 7x + 12) = 100

Reorder the terms:
4(12 + 7x + x2) = 100
(12 * 4 + 7x * 4 + x2 * 4) = 100
(48 + 28x + 4x2) = 100

Solving
48 + 28x + 4x2 = 100

Solving for variable 'x'.

Reorder the terms:
48 + -100 + 28x + 4x2 = 100 + -100

Combine like terms: 48 + -100 = -52
-52 + 28x + 4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-52 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-13 + 7x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-13 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + 7x + x2 = 0

Solving
-13 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 7x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 7x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 7x + x2 = 0 + 13
7x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
7x + x2 = 13

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 13 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 13 + 12.25

Combine like terms: 13 + 12.25 = 25.25
12.25 + 7x + x2 = 25.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
x + 3.5 = 5.024937811

Simplifying
x + 3.5 = 5.024937811

Reorder the terms:
3.5 + x = 5.024937811

Solving
3.5 + x = 5.024937811

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.024937811 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.024937811 + -3.5
x = 5.024937811 + -3.5

Combine like terms: 5.024937811 + -3.5 = 1.524937811
x = 1.524937811

Simplifying
x = 1.524937811


Subproblem 2
x + 3.5 = -5.024937811

Simplifying
x + 3.5 = -5.024937811

Reorder the terms:
3.5 + x = -5.024937811

Solving
3.5 + x = -5.024937811

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.024937811 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.024937811 + -3.5
x = -5.024937811 + -3.5

Combine like terms: -5.024937811 + -3.5 = -8.524937811
x = -8.524937811

Simplifying
x = -8.524937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.524937811, -8.524937811}
Solution
x = {1.524937811, -8.524937811}

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