x^2+3.5x=7

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Solution for x^2+3.5x=7 equation: 


Simplifying
x2 + 3.5x = 7

Reorder the terms:
3.5x + x2 = 7

Solving
3.5x + x2 = 7

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 7 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 7 + 3.0625

Combine like terms: 7 + 3.0625 = 10.0625
3.0625 + 3.5x + x2 = 10.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(x + 1.75) equal to 3.172144385 and -3.172144385.


Subproblem 1
x + 1.75 = 3.172144385

Simplifying
x + 1.75 = 3.172144385

Reorder the terms:
1.75 + x = 3.172144385

Solving
1.75 + x = 3.172144385

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 3.172144385 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 3.172144385 + -1.75
x = 3.172144385 + -1.75

Combine like terms: 3.172144385 + -1.75 = 1.422144385
x = 1.422144385

Simplifying
x = 1.422144385


Subproblem 2
x + 1.75 = -3.172144385

Simplifying
x + 1.75 = -3.172144385

Reorder the terms:
1.75 + x = -3.172144385

Solving
1.75 + x = -3.172144385

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -3.172144385 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -3.172144385 + -1.75
x = -3.172144385 + -1.75

Combine like terms: -3.172144385 + -1.75 = -4.922144385
x = -4.922144385

Simplifying
x = -4.922144385


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.422144385, -4.922144385}

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