x^2+1.5x-6.75=0

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Solution for x^2+1.5x-6.75=0 equation: 


Simplifying
x2 + 1.5x + -6.75 = 0

Reorder the terms:
-6.75 + 1.5x + x2 = 0

Solving
-6.75 + 1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + 1.5x + 6.75 + x2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + 1.5x + x2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + 1.5x + x2 = 0 + 6.75
1.5x + x2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
1.5x + x2 = 6.75

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 6.75 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 6.75 + 0.5625

Combine like terms: 6.75 + 0.5625 = 7.3125
0.5625 + 1.5x + x2 = 7.3125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 7.3125

Calculate the square root of the right side: 2.704163457

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.704163457 and -2.704163457.


Subproblem 1
x + 0.75 = 2.704163457

Simplifying
x + 0.75 = 2.704163457

Reorder the terms:
0.75 + x = 2.704163457

Solving
0.75 + x = 2.704163457

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.704163457 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.704163457 + -0.75
x = 2.704163457 + -0.75

Combine like terms: 2.704163457 + -0.75 = 1.954163457
x = 1.954163457

Simplifying
x = 1.954163457


Subproblem 2
x + 0.75 = -2.704163457

Simplifying
x + 0.75 = -2.704163457

Reorder the terms:
0.75 + x = -2.704163457

Solving
0.75 + x = -2.704163457

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.704163457 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.704163457 + -0.75
x = -2.704163457 + -0.75

Combine like terms: -2.704163457 + -0.75 = -3.454163457
x = -3.454163457

Simplifying
x = -3.454163457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.954163457, -3.454163457}

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