4y^2-7=y

Simple and best practice solution for 4y^2-7=y 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 4y^2-7=y equation:


Simplifying
4y2 + -7 = y

Reorder the terms:
-7 + 4y2 = y

Solving
-7 + 4y2 = y

Solving for variable 'y'.

Reorder the terms:
-7 + -1y + 4y2 = y + -1y

Combine like terms: y + -1y = 0
-7 + -1y + 4y2 = 0

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

Divide each side by '4'.
-1.75 + -0.25y + y2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.25y + 1.75 + y2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.25y + y2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.25y + y2 = 0 + 1.75
-0.25y + y2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.25y + y2 = 1.75

The y term is -0.25y.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25y + 0.015625 + y2 = 1.75 + 0.015625

Reorder the terms:
0.015625 + -0.25y + y2 = 1.75 + 0.015625

Combine like terms: 1.75 + 0.015625 = 1.765625
0.015625 + -0.25y + y2 = 1.765625

Factor a perfect square on the left side:
(y + -0.125)(y + -0.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(y + -0.125) equal to 1.328768227 and -1.328768227.

Subproblem 1

y + -0.125 = 1.328768227 Simplifying y + -0.125 = 1.328768227 Reorder the terms: -0.125 + y = 1.328768227 Solving -0.125 + y = 1.328768227 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 1.328768227 + 0.125 y = 1.328768227 + 0.125 Combine like terms: 1.328768227 + 0.125 = 1.453768227 y = 1.453768227 Simplifying y = 1.453768227

Subproblem 2

y + -0.125 = -1.328768227 Simplifying y + -0.125 = -1.328768227 Reorder the terms: -0.125 + y = -1.328768227 Solving -0.125 + y = -1.328768227 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -1.328768227 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -1.328768227 + 0.125 y = -1.328768227 + 0.125 Combine like terms: -1.328768227 + 0.125 = -1.203768227 y = -1.203768227 Simplifying y = -1.203768227

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.453768227, -1.203768227}

See similar equations:

| 9=x+20 | | (z-3)(z+2)=2z-3 | | (z-3)(z+2)=27-3 | | 5m^2-45= | | 9x=-153 | | -5(t-7)+5=-5 | | 3x-4=7-4x | | 98*8= | | z+.608695=.173913 | | 3x^2-19x+16=0 | | 3n+4(n-9)=78 | | -x-(13+4x)=3(5-9x+2) | | 4x+7(x-9)=47 | | -17x+20=7x-20 | | -6.7=1.3-4y | | -5(5x-1)+3=-25x+8 | | -5(3+d)=25 | | 4(x-7)+16=2(x-5) | | y=5x^2-25x+12 | | 5x-7-3x=3x-3 | | 5v^5-20v^4+20v^3= | | 16-5x=-7x+8 | | 9x+5=8x-2 | | 1.35x=70.2 | | ax+c=R | | 1.35x=54 | | (x^2-2x-35)-(x^2-7x)= | | -2f=7-f | | 13=15-4 | | 0.62x=1534.5 | | 6x-2=5x+6 | | 0.62x=3100 |

Equations solver categories