2x^2=14x-7

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Solution for 2x^2=14x-7 equation:


Simplifying
2x2 = 14x + -7

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

Solving
2x2 = -7 + 14x

Solving for variable 'x'.

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

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

Combine like terms: -7 + 7 = 0
7 + -14x + 2x2 = 0 + 14x + -14x
7 + -14x + 2x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
7 + -14x + 2x2 = 0

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 = 8.75
12.25 + -7x + x2 = 8.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

x + -3.5 = 2.958039892 Simplifying x + -3.5 = 2.958039892 Reorder the terms: -3.5 + x = 2.958039892 Solving -3.5 + x = 2.958039892 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 = 2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.958039892 + 3.5 x = 2.958039892 + 3.5 Combine like terms: 2.958039892 + 3.5 = 6.458039892 x = 6.458039892 Simplifying x = 6.458039892

Subproblem 2

x + -3.5 = -2.958039892 Simplifying x + -3.5 = -2.958039892 Reorder the terms: -3.5 + x = -2.958039892 Solving -3.5 + x = -2.958039892 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 = -2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.958039892 + 3.5 x = -2.958039892 + 3.5 Combine like terms: -2.958039892 + 3.5 = 0.541960108 x = 0.541960108 Simplifying x = 0.541960108

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.458039892, 0.541960108}

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