2*x^2+14*x-7=0

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Solution for 2*x^2+14*x-7=0 equation:


Simplifying
2x2 + 14x + -7 = 0

Reorder the terms:
-7 + 14x + 2x2 = 0

Solving
-7 + 14x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-3.5 + 7x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 7x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 7x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 7x + x2 = 0 + 3.5
7x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
7x + x2 = 3.5

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 = 3.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 3.5 + 12.25

Combine like terms: 3.5 + 12.25 = 15.75
12.25 + 7x + x2 = 15.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 15.75

Calculate the square root of the right side: 3.968626967

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.968626967 and -3.968626967.

Subproblem 1

x + 3.5 = 3.968626967 Simplifying x + 3.5 = 3.968626967 Reorder the terms: 3.5 + x = 3.968626967 Solving 3.5 + x = 3.968626967 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 = 3.968626967 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.968626967 + -3.5 x = 3.968626967 + -3.5 Combine like terms: 3.968626967 + -3.5 = 0.468626967 x = 0.468626967 Simplifying x = 0.468626967

Subproblem 2

x + 3.5 = -3.968626967 Simplifying x + 3.5 = -3.968626967 Reorder the terms: 3.5 + x = -3.968626967 Solving 3.5 + x = -3.968626967 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 = -3.968626967 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.968626967 + -3.5 x = -3.968626967 + -3.5 Combine like terms: -3.968626967 + -3.5 = -7.468626967 x = -7.468626967 Simplifying x = -7.468626967

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.468626967, -7.468626967}

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