y^2+1.53y-1.74=0

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Solution for y^2+1.53y-1.74=0 equation: 


Simplifying
y2 + 1.53y + -1.74 = 0

Reorder the terms:
-1.74 + 1.53y + y2 = 0

Solving
-1.74 + 1.53y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1.74' to each side of the equation.
-1.74 + 1.53y + 1.74 + y2 = 0 + 1.74

Reorder the terms:
-1.74 + 1.74 + 1.53y + y2 = 0 + 1.74

Combine like terms: -1.74 + 1.74 = 0.00
0.00 + 1.53y + y2 = 0 + 1.74
1.53y + y2 = 0 + 1.74

Combine like terms: 0 + 1.74 = 1.74
1.53y + y2 = 1.74

The y term is 1.53y.  Take half its coefficient (0.765).
Square it (0.585225) and add it to both sides.

Add '0.585225' to each side of the equation.
1.53y + 0.585225 + y2 = 1.74 + 0.585225

Reorder the terms:
0.585225 + 1.53y + y2 = 1.74 + 0.585225

Combine like terms: 1.74 + 0.585225 = 2.325225
0.585225 + 1.53y + y2 = 2.325225

Factor a perfect square on the left side:
(y + 0.765)(y + 0.765) = 2.325225

Calculate the square root of the right side: 1.524868847

Break this problem into two subproblems by setting 
(y + 0.765) equal to 1.524868847 and -1.524868847.


Subproblem 1
y + 0.765 = 1.524868847

Simplifying
y + 0.765 = 1.524868847

Reorder the terms:
0.765 + y = 1.524868847

Solving
0.765 + y = 1.524868847

Solving for variable 'y'.

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

Add '-0.765' to each side of the equation.
0.765 + -0.765 + y = 1.524868847 + -0.765

Combine like terms: 0.765 + -0.765 = 0.000
0.000 + y = 1.524868847 + -0.765
y = 1.524868847 + -0.765

Combine like terms: 1.524868847 + -0.765 = 0.759868847
y = 0.759868847

Simplifying
y = 0.759868847


Subproblem 2
y + 0.765 = -1.524868847

Simplifying
y + 0.765 = -1.524868847

Reorder the terms:
0.765 + y = -1.524868847

Solving
0.765 + y = -1.524868847

Solving for variable 'y'.

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

Add '-0.765' to each side of the equation.
0.765 + -0.765 + y = -1.524868847 + -0.765

Combine like terms: 0.765 + -0.765 = 0.000
0.000 + y = -1.524868847 + -0.765
y = -1.524868847 + -0.765

Combine like terms: -1.524868847 + -0.765 = -2.289868847
y = -2.289868847

Simplifying
y = -2.289868847


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.759868847, -2.289868847}

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