y^2+3y=7

Simple and best practice solution for y^2+3y=7 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+3y=7 equation:


Simplifying
y2 + 3y = 7

Reorder the terms:
3y + y2 = 7

Solving
3y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + 3y + y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + 3y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3y + y2 = 0 + 7
3y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
3y + y2 = 7

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 7 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + 3y + y2 = 9.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + 1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

y + 1.5 = 3.041381265 Simplifying y + 1.5 = 3.041381265 Reorder the terms: 1.5 + y = 3.041381265 Solving 1.5 + y = 3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 3.041381265 + -1.5 y = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 y = 1.541381265 Simplifying y = 1.541381265

Subproblem 2

y + 1.5 = -3.041381265 Simplifying y + 1.5 = -3.041381265 Reorder the terms: 1.5 + y = -3.041381265 Solving 1.5 + y = -3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -3.041381265 + -1.5 y = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 y = -4.541381265 Simplifying y = -4.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.541381265, -4.541381265}

See similar equations:

| 7a-3=3m-31 | | (Y^3+1)+((y^2+1)+(3y-7))=0 | | -31+4Y+2=2(3Y-3)-5 | | 4x(x-8)=2(2x-1)(x-9) | | -5(d+1)=-25 | | (15x^4-18x-19)-(13x^4-5x+15)=0 | | .25y-3=.16y | | 3(C-2)+3=2+C-5 | | x+3(x+3)=46 | | 0.7z+1.9+0.1z=5.5-0.47 | | 5-(-y+6)=2(-y+3)-7(y+1) | | 9-5X=18+4X | | 69=3x+15 | | m/12+4=-6 | | 56c^2-23c=63 | | .1(h+20)=3 | | 4+(3x-7)=7x+7 | | n-7-n=81+81n-8n-88 | | 2x=136 | | m/9-1=-3 | | 2x=137 | | 2x=142 | | 6x+1=11x-29 | | 9(x+7)+4=-11(x-5)-4 | | 5x-33=-6x | | (5v+2)(2v-2y-7)=0 | | -2Y-12=5Y+23 | | v+(v-32.3)+(v+26.2)=195.8 | | -5x+6=-x+8 | | 4w^4-81= | | x+5x=168 | | 4(x+4)=3[x-(3-x)] |

Equations solver categories