y^2+y-7=0

Simple and best practice solution for y^2+y-7=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+y-7=0 equation:


Simplifying
y2 + y + -7 = 0

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

Solving
-7 + y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 7 + 0.25

Reorder the terms:
0.25 + y + y2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + y + y2 = 7.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

y + 0.5 = 2.692582404 Simplifying y + 0.5 = 2.692582404 Reorder the terms: 0.5 + y = 2.692582404 Solving 0.5 + y = 2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.692582404 + -0.5 y = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 y = 2.192582404 Simplifying y = 2.192582404

Subproblem 2

y + 0.5 = -2.692582404 Simplifying y + 0.5 = -2.692582404 Reorder the terms: 0.5 + y = -2.692582404 Solving 0.5 + y = -2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.692582404 + -0.5 y = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 y = -3.192582404 Simplifying y = -3.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. y = {2.192582404, -3.192582404}

See similar equations:

| -2/5x-1/9x-7/5 | | 5/6x-1/3=19/3 | | 1.7=3.17+0.6m | | 1/3(2x-9) | | 1/5=-1/8x+3/5 | | 16w^2-40wg+25g^2=0 | | C=12+2.50h | | -5/9x-1/8x-7/9 | | 3/4x-1/3=17/3 | | 5/6x-1/2=17/6 | | 1142=16t^2 | | 3x^4=-48 | | (x+1)+(x+2)=319 | | 2.1=2.59+0.2m | | (x+1)+(x+2)=331 | | 11=164+40 | | 6m+mn+54+9n=0 | | 1/2(8x-10)=1/4(20x-16) | | 7x^2=2 | | 2/3x+4/x=7/x+1 | | 4+2x/7+5-x/5=34/35 | | 2(x+2)=3(x-3) | | 3+2x/7+4-x/2=19/14 | | 3x+1/2=x-4/5 | | -6x-15=3x+12 | | p-2=p+1 | | .22-.02(x+2)=-.04(3-x) | | 2x^2-10x=-360 | | x^2-5x=-180 | | 23-(x+6)=4x-3 | | 4(3k-2)=5(k+4) | | 5(x-8)+15=3(x-5) |

Equations solver categories