2x^2+14x+7x=49

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Solution for 2x^2+14x+7x=49 equation:


Simplifying
2x2 + 14x + 7x = 49

Reorder the terms:
14x + 7x + 2x2 = 49

Combine like terms: 14x + 7x = 21x
21x + 2x2 = 49

Solving
21x + 2x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + 21x + 2x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 21x + 2x2 = 0

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

Divide each side by '2'.
-24.5 + 10.5x + x2 = 0

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + 10.5x + 24.5 + x2 = 0 + 24.5

Reorder the terms:
-24.5 + 24.5 + 10.5x + x2 = 0 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + 10.5x + x2 = 0 + 24.5
10.5x + x2 = 0 + 24.5

Combine like terms: 0 + 24.5 = 24.5
10.5x + x2 = 24.5

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 24.5 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 24.5 + 27.5625

Combine like terms: 24.5 + 27.5625 = 52.0625
27.5625 + 10.5x + x2 = 52.0625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 52.0625

Calculate the square root of the right side: 7.215434845

Break this problem into two subproblems by setting 
(x + 5.25) equal to 7.215434845 and -7.215434845.

Subproblem 1

x + 5.25 = 7.215434845 Simplifying x + 5.25 = 7.215434845 Reorder the terms: 5.25 + x = 7.215434845 Solving 5.25 + x = 7.215434845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 7.215434845 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 7.215434845 + -5.25 x = 7.215434845 + -5.25 Combine like terms: 7.215434845 + -5.25 = 1.965434845 x = 1.965434845 Simplifying x = 1.965434845

Subproblem 2

x + 5.25 = -7.215434845 Simplifying x + 5.25 = -7.215434845 Reorder the terms: 5.25 + x = -7.215434845 Solving 5.25 + x = -7.215434845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -7.215434845 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -7.215434845 + -5.25 x = -7.215434845 + -5.25 Combine like terms: -7.215434845 + -5.25 = -12.465434845 x = -12.465434845 Simplifying x = -12.465434845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.965434845, -12.465434845}

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