q^2+5q=90

Simple and best practice solution for q^2+5q=90 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 q^2+5q=90 equation: 


Simplifying
q2 + 5q = 90

Reorder the terms:
5q + q2 = 90

Solving
5q + q2 = 90

Solving for variable 'q'.

Reorder the terms:
-90 + 5q + q2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 5q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 5q + 90 + q2 = 0 + 90

Reorder the terms:
-90 + 90 + 5q + q2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 5q + q2 = 0 + 90
5q + q2 = 0 + 90

Combine like terms: 0 + 90 = 90
5q + q2 = 90

The q term is 5q.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5q + 6.25 + q2 = 90 + 6.25

Reorder the terms:
6.25 + 5q + q2 = 90 + 6.25

Combine like terms: 90 + 6.25 = 96.25
6.25 + 5q + q2 = 96.25

Factor a perfect square on the left side:
(q + 2.5)(q + 2.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(q + 2.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
q + 2.5 = 9.810708435

Simplifying
q + 2.5 = 9.810708435

Reorder the terms:
2.5 + q = 9.810708435

Solving
2.5 + q = 9.810708435

Solving for variable 'q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = 9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = 9.810708435 + -2.5
q = 9.810708435 + -2.5

Combine like terms: 9.810708435 + -2.5 = 7.310708435
q = 7.310708435

Simplifying
q = 7.310708435


Subproblem 2
q + 2.5 = -9.810708435

Simplifying
q + 2.5 = -9.810708435

Reorder the terms:
2.5 + q = -9.810708435

Solving
2.5 + q = -9.810708435

Solving for variable 'q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + q = -9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + q = -9.810708435 + -2.5
q = -9.810708435 + -2.5

Combine like terms: -9.810708435 + -2.5 = -12.310708435
q = -12.310708435

Simplifying
q = -12.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {7.310708435, -12.310708435}

See similar equations:

| X^3-1-7=0 | | 5+55x=33x+23 | | 6x+1=8.9 | | 6(x-9)=21.83 | | (x^2-2xy)dx+xdy=0 | | x-8y^2+2xy^2-4=0 | | -2.5=p+7.7 | | 3y-5+7=8 | | 7w-3w+2w=-3w+40-w | | 22y=-2y-96 | | 2x+1-4x=11 | | -1+31=-7-7a-8-2a | | 2x-3=6x-3-4x | | 10t^2=13t-4 | | b+15=3 | | -8x-16=-16 | | 2h=-1.46 | | (3x-20)= | | 6d^2=20-7d | | x=4x-10(-2) | | 5(1+6d)=-33 | | 6(3-3t)-1=5 | | 9x=5x+x+3x | | 11v=-121 | | 24k+132=24k+132 | | -5x+3+8x+10=-5+30 | | x^6-25x^8=0 | | (x)=3-5x | | 1.9z-19=3.8 | | 25x+58+12x=62 | | 3x^2+6x-kx+12=0 | | 5x-76=x |

Equations solver categories