2x^2+14x=35

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Solution for 2x^2+14x=35 equation:


Simplifying
2x2 + 14x = 35

Reorder the terms:
14x + 2x2 = 35

Solving
14x + 2x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + 14x + 2x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 14x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + 7x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 7x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 7x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 7x + x2 = 0 + 17.5
7x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
7x + x2 = 17.5

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 = 17.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 17.5 + 12.25

Combine like terms: 17.5 + 12.25 = 29.75
12.25 + 7x + x2 = 29.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 29.75

Calculate the square root of the right side: 5.454356057

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.454356057 and -5.454356057.

Subproblem 1

x + 3.5 = 5.454356057 Simplifying x + 3.5 = 5.454356057 Reorder the terms: 3.5 + x = 5.454356057 Solving 3.5 + x = 5.454356057 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 = 5.454356057 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.454356057 + -3.5 x = 5.454356057 + -3.5 Combine like terms: 5.454356057 + -3.5 = 1.954356057 x = 1.954356057 Simplifying x = 1.954356057

Subproblem 2

x + 3.5 = -5.454356057 Simplifying x + 3.5 = -5.454356057 Reorder the terms: 3.5 + x = -5.454356057 Solving 3.5 + x = -5.454356057 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 = -5.454356057 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.454356057 + -3.5 x = -5.454356057 + -3.5 Combine like terms: -5.454356057 + -3.5 = -8.954356057 x = -8.954356057 Simplifying x = -8.954356057

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.954356057, -8.954356057}

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