2x^2+6x=7

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Solution for 2x^2+6x=7 equation:


Simplifying
2x2 + 6x = 7

Reorder the terms:
6x + 2x2 = 7

Solving
6x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 6x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 6x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 3x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 3x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 3x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 3x + x2 = 0 + 3.5
3x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
3x + x2 = 3.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 3.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + 3x + x2 = 5.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.397915762 and -2.397915762.

Subproblem 1

x + 1.5 = 2.397915762 Simplifying x + 1.5 = 2.397915762 Reorder the terms: 1.5 + x = 2.397915762 Solving 1.5 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.397915762 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.397915762 + -1.5 x = 2.397915762 + -1.5 Combine like terms: 2.397915762 + -1.5 = 0.897915762 x = 0.897915762 Simplifying x = 0.897915762

Subproblem 2

x + 1.5 = -2.397915762 Simplifying x + 1.5 = -2.397915762 Reorder the terms: 1.5 + x = -2.397915762 Solving 1.5 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.397915762 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.397915762 + -1.5 x = -2.397915762 + -1.5 Combine like terms: -2.397915762 + -1.5 = -3.897915762 x = -3.897915762 Simplifying x = -3.897915762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.897915762, -3.897915762}

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