10x^2+3x-54=0

Simple and best practice solution for 10x^2+3x-54=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 10x^2+3x-54=0 equation: 


Simplifying
10x2 + 3x + -54 = 0

Reorder the terms:
-54 + 3x + 10x2 = 0

Solving
-54 + 3x + 10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-5.4 + 0.3x + x2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + 0.3x + 5.4 + x2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + 0.3x + x2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + 0.3x + x2 = 0 + 5.4
0.3x + x2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
0.3x + x2 = 5.4

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 5.4 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 5.4 + 0.0225

Combine like terms: 5.4 + 0.0225 = 5.4225
0.0225 + 0.3x + x2 = 5.4225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 5.4225

Calculate the square root of the right side: 2.328626204

Break this problem into two subproblems by setting 
(x + 0.15) equal to 2.328626204 and -2.328626204.


Subproblem 1
x + 0.15 = 2.328626204

Simplifying
x + 0.15 = 2.328626204

Reorder the terms:
0.15 + x = 2.328626204

Solving
0.15 + x = 2.328626204

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 2.328626204 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 2.328626204 + -0.15
x = 2.328626204 + -0.15

Combine like terms: 2.328626204 + -0.15 = 2.178626204
x = 2.178626204

Simplifying
x = 2.178626204


Subproblem 2
x + 0.15 = -2.328626204

Simplifying
x + 0.15 = -2.328626204

Reorder the terms:
0.15 + x = -2.328626204

Solving
0.15 + x = -2.328626204

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -2.328626204 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -2.328626204 + -0.15
x = -2.328626204 + -0.15

Combine like terms: -2.328626204 + -0.15 = -2.478626204
x = -2.478626204

Simplifying
x = -2.478626204


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.178626204, -2.478626204}

See similar equations:

| v/13=4/5 | | 2w+8=24 | | 5x+34=10+8x | | y+n=53 | | yn+5=53 | | 1[x+7]=14 | | -4*2x+-4*-6=10x | | 5[x+7]=25 | | 4[x-12]=12 | | 1500=600/t | | 6x^2-58x+104=0 | | (2ab)(3ab)= | | t+600=1500 | | 1500=t/600 | | 1.96+-0.825= | | a=1/2bc^2 | | 600+t=1500 | | 1+1+1+1+1+1+1*0+1=X | | 4x+50-y=180 | | 1+1+1+1+1+1+1*1+1=X | | 35k^2-37k-6=0 | | 1+1+1+1+1+1+1*1+1= | | -0.5(y-12)=0.1(y+1) | | 1500=600+t | | 7k^2-6k-16=0 | | [4](1[v-9]1)=2v-18 | | x^2-5x-32=-8 | | 4x+y=1000 | | 11-14=19 | | 6u-8=4(u+1) | | r^2-10r+8=-8 | | 7x+2=75 |

Equations solver categories