X*X+5X=60

Simple and best practice solution for X*X+5X=60 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 X*X+5X=60 equation:


Simplifying
X * X + 5X = 60

Multiply X * X
X2 + 5X = 60

Reorder the terms:
5X + X2 = 60

Solving
5X + X2 = 60

Solving for variable 'X'.

Reorder the terms:
-60 + 5X + X2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 5X + 60 + X2 = 0 + 60

Reorder the terms:
-60 + 60 + 5X + X2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 5X + X2 = 0 + 60
5X + X2 = 0 + 60

Combine like terms: 0 + 60 = 60
5X + X2 = 60

The X term is 5X.  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.
5X + 6.25 + X2 = 60 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 60 + 6.25

Combine like terms: 60 + 6.25 = 66.25
6.25 + 5X + X2 = 66.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(X + 2.5) equal to 8.139410298 and -8.139410298.

Subproblem 1

X + 2.5 = 8.139410298 Simplifying X + 2.5 = 8.139410298 Reorder the terms: 2.5 + X = 8.139410298 Solving 2.5 + X = 8.139410298 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = 8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 8.139410298 + -2.5 X = 8.139410298 + -2.5 Combine like terms: 8.139410298 + -2.5 = 5.639410298 X = 5.639410298 Simplifying X = 5.639410298

Subproblem 2

X + 2.5 = -8.139410298 Simplifying X + 2.5 = -8.139410298 Reorder the terms: 2.5 + X = -8.139410298 Solving 2.5 + X = -8.139410298 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = -8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -8.139410298 + -2.5 X = -8.139410298 + -2.5 Combine like terms: -8.139410298 + -2.5 = -10.639410298 X = -10.639410298 Simplifying X = -10.639410298

Solution

The solution to the problem is based on the solutions from the subproblems. X = {5.639410298, -10.639410298}

See similar equations:

| x^2-4x=20+0 | | v+2/7+3/7=-1/7(v-5/2) | | (5)(3ABC)= | | 3/5g+9-2/5g=30 | | 7t+10t=136 | | 4/x=4/5 | | 3/5k+1/5k=4 | | 7v-8=27 | | n-3/n+3+1/n-3=18/n^2-9 | | 5x+12=-4x+12 | | z/5=-25 | | -9v+14=5v+14 | | 3w-20=5w | | 3(2x+11)=3 | | 2.5-3.4-1.24=6.7-9.1+1.34 | | 180-7= | | 2(x+4)-8(9x-8)=15 | | -4c=-80 | | d+3.95+0.25d=7.70 | | 2x-6=14-3x | | -5(3b+2)+(16b-3)=0 | | 1/15+1/18=11 | | y=4/3x+2 | | t^7/(4y+6t)^7 | | 3.2q-3.6-5.2q=3.0q-3.9 | | =45x^2-72x+24 | | 4x+6=12-1x | | 15m+12n+5m-3n= | | 4x+2=6-2x | | 128x^2-16x+1=0 | | -2y-13=4y+11 | | y+7/5y-4 |

Equations solver categories