2y^2+4y-7=y^2+1

Simple and best practice solution for 2y^2+4y-7=y^2+1 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 2y^2+4y-7=y^2+1 equation:


Simplifying
2y2 + 4y + -7 = y2 + 1

Reorder the terms:
-7 + 4y + 2y2 = y2 + 1

Reorder the terms:
-7 + 4y + 2y2 = 1 + y2

Solving
-7 + 4y + 2y2 = 1 + y2

Solving for variable 'y'.

Reorder the terms:
-7 + -1 + 4y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2

Combine like terms: -7 + -1 = -8
-8 + 4y + 2y2 + -1y2 = 1 + y2 + -1 + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-8 + 4y + 1y2 = 1 + y2 + -1 + -1y2

Reorder the terms:
-8 + 4y + 1y2 = 1 + -1 + y2 + -1y2

Combine like terms: 1 + -1 = 0
-8 + 4y + 1y2 = 0 + y2 + -1y2
-8 + 4y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-8 + 4y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + 4y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 4y + y2 = 0 + 8
4y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
4y + y2 = 8

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 8 + 4

Reorder the terms:
4 + 4y + y2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + 4y + y2 = 12

Factor a perfect square on the left side:
(y + 2)(y + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + 2) equal to 3.464101615 and -3.464101615.

Subproblem 1

y + 2 = 3.464101615 Simplifying y + 2 = 3.464101615 Reorder the terms: 2 + y = 3.464101615 Solving 2 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.464101615 + -2 y = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 y = 1.464101615 Simplifying y = 1.464101615

Subproblem 2

y + 2 = -3.464101615 Simplifying y + 2 = -3.464101615 Reorder the terms: 2 + y = -3.464101615 Solving 2 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.464101615 + -2 y = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 y = -5.464101615 Simplifying y = -5.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.464101615, -5.464101615}

See similar equations:

| 11x+8y=-24 | | y=0.69x+4.29 | | 3x+7-x=3 | | ln(6x^2+5x)=0 | | -4(x-2)=4x | | 4x^2-25y^2=11 | | 4x+4(2x-15)=60 | | 4x^2+36x-47=0 | | 33=y+39 | | -5=r-6 | | 5(n+7)=75 | | 36*30x=45 | | (-66)+(-13)=c | | -3(1-n)=2(2+1) | | 6.4/.02 | | 6=1g+10-3g | | y=4x^2-2x+10 | | 4z-6-5z= | | 16(n-7)=-4(n+38) | | 0.5a-6=0.2a | | -3.5q+1.4=-20.6-1.3q | | 5x-2=6 | | 4(n-4)=-2(n-19) | | A+(-47)=68 | | -n^2-15n+50=0 | | 2(4-k)+k=7 | | 12(n-2)=-4(n+10) | | 2x/5-×/3=5 | | 36000/120 | | 12(n+8)=-3(n-47) | | 6b^2+13v-6=-12 | | -8b+9+6=-3b+14 |

Equations solver categories