21y^2-70y+40=

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Solution for 21y^2-70y+40= equation:


Simplifying
21y2 + -70y + 40 = 0

Reorder the terms:
40 + -70y + 21y2 = 0

Solving
40 + -70y + 21y2 = 0

Solving for variable 'y'.

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

Divide each side by '21'.
1.904761905 + -3.333333333y + y2 = 0

Move the constant term to the right:

Add '-1.904761905' to each side of the equation.
1.904761905 + -3.333333333y + -1.904761905 + y2 = 0 + -1.904761905

Reorder the terms:
1.904761905 + -1.904761905 + -3.333333333y + y2 = 0 + -1.904761905

Combine like terms: 1.904761905 + -1.904761905 = 0.000000000
0.000000000 + -3.333333333y + y2 = 0 + -1.904761905
-3.333333333y + y2 = 0 + -1.904761905

Combine like terms: 0 + -1.904761905 = -1.904761905
-3.333333333y + y2 = -1.904761905

The y term is -3.333333333y.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333y + 2.777777779 + y2 = -1.904761905 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333y + y2 = -1.904761905 + 2.777777779

Combine like terms: -1.904761905 + 2.777777779 = 0.873015874
2.777777779 + -3.333333333y + y2 = 0.873015874

Factor a perfect square on the left side:
(y + -1.666666667)(y + -1.666666667) = 0.873015874

Calculate the square root of the right side: 0.934353185

Break this problem into two subproblems by setting 
(y + -1.666666667) equal to 0.934353185 and -0.934353185.

Subproblem 1

y + -1.666666667 = 0.934353185 Simplifying y + -1.666666667 = 0.934353185 Reorder the terms: -1.666666667 + y = 0.934353185 Solving -1.666666667 + y = 0.934353185 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = 0.934353185 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = 0.934353185 + 1.666666667 y = 0.934353185 + 1.666666667 Combine like terms: 0.934353185 + 1.666666667 = 2.601019852 y = 2.601019852 Simplifying y = 2.601019852

Subproblem 2

y + -1.666666667 = -0.934353185 Simplifying y + -1.666666667 = -0.934353185 Reorder the terms: -1.666666667 + y = -0.934353185 Solving -1.666666667 + y = -0.934353185 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + y = -0.934353185 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + y = -0.934353185 + 1.666666667 y = -0.934353185 + 1.666666667 Combine like terms: -0.934353185 + 1.666666667 = 0.732313482 y = 0.732313482 Simplifying y = 0.732313482

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.601019852, 0.732313482}

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