x^2+5x=1.5

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Solution for x^2+5x=1.5 equation: 


Simplifying
x2 + 5x = 1.5

Reorder the terms:
5x + x2 = 1.5

Solving
5x + x2 = 1.5

Solving for variable 'x'.

Reorder the terms:
-1.5 + 5x + x2 = 1.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + 5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 5x + 1.5 + x2 = 0.0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 5x + x2 = 0.0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 5x + x2 = 0.0 + 1.5
5x + x2 = 0.0 + 1.5

Combine like terms: 0.0 + 1.5 = 1.5
5x + x2 = 1.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 1.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1.5 + 6.25

Combine like terms: 1.5 + 6.25 = 7.75
6.25 + 5x + x2 = 7.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.783882181 and -2.783882181.


Subproblem 1
x + 2.5 = 2.783882181

Simplifying
x + 2.5 = 2.783882181

Reorder the terms:
2.5 + x = 2.783882181

Solving
2.5 + x = 2.783882181

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.783882181 + -2.5
x = 2.783882181 + -2.5

Combine like terms: 2.783882181 + -2.5 = 0.283882181
x = 0.283882181

Simplifying
x = 0.283882181


Subproblem 2
x + 2.5 = -2.783882181

Simplifying
x + 2.5 = -2.783882181

Reorder the terms:
2.5 + x = -2.783882181

Solving
2.5 + x = -2.783882181

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.783882181 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.783882181 + -2.5
x = -2.783882181 + -2.5

Combine like terms: -2.783882181 + -2.5 = -5.283882181
x = -5.283882181

Simplifying
x = -5.283882181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.283882181, -5.283882181}

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