y^2-35y+178=0

Simple and best practice solution for y^2-35y+178=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for y^2-35y+178=0 equation: 


Simplifying
y2 + -35y + 178 = 0

Reorder the terms:
178 + -35y + y2 = 0

Solving
178 + -35y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-178' to each side of the equation.
178 + -35y + -178 + y2 = 0 + -178

Reorder the terms:
178 + -178 + -35y + y2 = 0 + -178

Combine like terms: 178 + -178 = 0
0 + -35y + y2 = 0 + -178
-35y + y2 = 0 + -178

Combine like terms: 0 + -178 = -178
-35y + y2 = -178

The y term is -35y.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35y + 306.25 + y2 = -178 + 306.25

Reorder the terms:
306.25 + -35y + y2 = -178 + 306.25

Combine like terms: -178 + 306.25 = 128.25
306.25 + -35y + y2 = 128.25

Factor a perfect square on the left side:
(y + -17.5)(y + -17.5) = 128.25

Calculate the square root of the right side: 11.324751653

Break this problem into two subproblems by setting 
(y + -17.5) equal to 11.324751653 and -11.324751653.


Subproblem 1
y + -17.5 = 11.324751653

Simplifying
y + -17.5 = 11.324751653

Reorder the terms:
-17.5 + y = 11.324751653

Solving
-17.5 + y = 11.324751653

Solving for variable 'y'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + y = 11.324751653 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + y = 11.324751653 + 17.5
y = 11.324751653 + 17.5

Combine like terms: 11.324751653 + 17.5 = 28.824751653
y = 28.824751653

Simplifying
y = 28.824751653


Subproblem 2
y + -17.5 = -11.324751653

Simplifying
y + -17.5 = -11.324751653

Reorder the terms:
-17.5 + y = -11.324751653

Solving
-17.5 + y = -11.324751653

Solving for variable 'y'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + y = -11.324751653 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + y = -11.324751653 + 17.5
y = -11.324751653 + 17.5

Combine like terms: -11.324751653 + 17.5 = 6.175248347
y = 6.175248347

Simplifying
y = 6.175248347


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {28.824751653, 6.175248347}

See similar equations:

| (e+1)*5=20 | | x^5+4X^3-27=0 | | log[3](x^2+45)=2+log[3](2x) | | 9c-4=20-3c | | F(x)=4x^2 | | 12p+15=99 | | d^2+23d=50 | | 21x+33= | | 2u+3=8 | | (2x-4)(3x-6)+4=0 | | 9r-81= | | (-9)-(-3)+(-5)-(-1)= | | 12y+16= | | -8x-32=12-3x | | 4x+4y-3y-x+4= | | 70-7c= | | 6t-2=5t-14 | | (-4)+(-7)(-6)-(-8)= | | 9s-17=19 | | ln(5x+12)+ln(5x-12)=ln(81) | | 9i+63= | | (-3)-(-5)+(-4)-(-2)= | | f(x)=8x^3-22x^2-4 | | 50+5f= | | (w*3)+(1-w)*11=7 | | (-1)+(-6)-(-7)-(-9)= | | solve(w*3)+(1-w)*11=7 | | 4e+2=22 | | 7n+1-3n+4= | | 12n+60= | | 4x^2-4xp+p^2=4x^2+kx+9 | | (-6)+(-8)-(-5)-(-1)= |

Equations solver categories