7y^2-7y-15=0

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Solution for 7y^2-7y-15=0 equation:


Simplifying
7y2 + -7y + -15 = 0

Reorder the terms:
-15 + -7y + 7y2 = 0

Solving
-15 + -7y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
-2.142857143 + -1y + y2 = 0

Move the constant term to the right:

Add '2.142857143' to each side of the equation.
-2.142857143 + -1y + 2.142857143 + y2 = 0 + 2.142857143

Reorder the terms:
-2.142857143 + 2.142857143 + -1y + y2 = 0 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + -1y + y2 = 0 + 2.142857143
-1y + y2 = 0 + 2.142857143

Combine like terms: 0 + 2.142857143 = 2.142857143
-1y + y2 = 2.142857143

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 2.142857143 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 2.142857143 + 0.25

Combine like terms: 2.142857143 + 0.25 = 2.392857143
0.25 + -1y + y2 = 2.392857143

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 2.392857143

Calculate the square root of the right side: 1.546886273

Break this problem into two subproblems by setting 
(y + -0.5) equal to 1.546886273 and -1.546886273.

Subproblem 1

y + -0.5 = 1.546886273 Simplifying y + -0.5 = 1.546886273 Reorder the terms: -0.5 + y = 1.546886273 Solving -0.5 + y = 1.546886273 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.546886273 + 0.5 y = 1.546886273 + 0.5 Combine like terms: 1.546886273 + 0.5 = 2.046886273 y = 2.046886273 Simplifying y = 2.046886273

Subproblem 2

y + -0.5 = -1.546886273 Simplifying y + -0.5 = -1.546886273 Reorder the terms: -0.5 + y = -1.546886273 Solving -0.5 + y = -1.546886273 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.546886273 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.546886273 + 0.5 y = -1.546886273 + 0.5 Combine like terms: -1.546886273 + 0.5 = -1.046886273 y = -1.046886273 Simplifying y = -1.046886273

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.046886273, -1.046886273}

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