.62(x-1.5)(x-1.5)-2.71=7

Solution for .62(x-1.5)(x-1.5)-2.71=7 equation:

Simplifying
0.62(x + -1.5)(x + -1.5) + -2.71 = 7

Reorder the terms:
0.62(-1.5 + x)(x + -1.5) + -2.71 = 7

Reorder the terms:
0.62(-1.5 + x)(-1.5 + x) + -2.71 = 7

Multiply (-1.5 + x) * (-1.5 + x)
0.62(-1.5(-1.5 + x) + x(-1.5 + x)) + -2.71 = 7
0.62((-1.5 * -1.5 + x * -1.5) + x(-1.5 + x)) + -2.71 = 7
0.62((2.25 + -1.5x) + x(-1.5 + x)) + -2.71 = 7
0.62(2.25 + -1.5x + (-1.5 * x + x * x)) + -2.71 = 7
0.62(2.25 + -1.5x + (-1.5x + x2)) + -2.71 = 7

Combine like terms: -1.5x + -1.5x = -3x
0.62(2.25 + -3x + x2) + -2.71 = 7
(2.25 * 0.62 + -3x * 0.62 + x2 * 0.62) + -2.71 = 7
(1.395 + -1.86x + 0.62x2) + -2.71 = 7

Reorder the terms:
1.395 + -2.71 + -1.86x + 0.62x2 = 7

Combine like terms: 1.395 + -2.71 = -1.315
-1.315 + -1.86x + 0.62x2 = 7

Solving
-1.315 + -1.86x + 0.62x2 = 7

Solving for variable 'x'.

Reorder the terms:
-1.315 + -7 + -1.86x + 0.62x2 = 7 + -7

Combine like terms: -1.315 + -7 = -8.315
-8.315 + -1.86x + 0.62x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-8.315 + -1.86x + 0.62x2 = 0

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

Divide each side by '0.62'.
-13.41129032 + -3x + x2 = 0

Move the constant term to the right:

Add '13.41129032' to each side of the equation.
-13.41129032 + -3x + 13.41129032 + x2 = 0 + 13.41129032

Reorder the terms:
-13.41129032 + 13.41129032 + -3x + x2 = 0 + 13.41129032

Combine like terms: -13.41129032 + 13.41129032 = 0.00000000
0.00000000 + -3x + x2 = 0 + 13.41129032
-3x + x2 = 0 + 13.41129032

Combine like terms: 0 + 13.41129032 = 13.41129032
-3x + x2 = 13.41129032

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 = 13.41129032 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 13.41129032 + 2.25

Combine like terms: 13.41129032 + 2.25 = 15.66129032
2.25 + -3x + x2 = 15.66129032

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 15.66129032

Calculate the square root of the right side: 3.957434816

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.957434816 and -3.957434816.

Subproblem 1
x + -1.5 = 3.957434816

Simplifying
x + -1.5 = 3.957434816

Reorder the terms:
-1.5 + x = 3.957434816

Solving
-1.5 + x = 3.957434816

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 = 3.957434816 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.957434816 + 1.5
x = 3.957434816 + 1.5

Combine like terms: 3.957434816 + 1.5 = 5.457434816
x = 5.457434816

Simplifying
x = 5.457434816

Subproblem 2
x + -1.5 = -3.957434816

Simplifying
x + -1.5 = -3.957434816

Reorder the terms:
-1.5 + x = -3.957434816

Solving
-1.5 + x = -3.957434816

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 = -3.957434816 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.957434816 + 1.5
x = -3.957434816 + 1.5

Combine like terms: -3.957434816 + 1.5 = -2.457434816
x = -2.457434816

Simplifying
x = -2.457434816

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.457434816, -2.457434816}