3x^2-3x+7=-24x+4

Simple and best practice solution for 3x^2-3x+7=-24x+4 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 3x^2-3x+7=-24x+4 equation: 


Simplifying
3x2 + -3x + 7 = -24x + 4

Reorder the terms:
7 + -3x + 3x2 = -24x + 4

Reorder the terms:
7 + -3x + 3x2 = 4 + -24x

Solving
7 + -3x + 3x2 = 4 + -24x

Solving for variable 'x'.

Reorder the terms:
7 + -4 + -3x + 24x + 3x2 = 4 + -24x + -4 + 24x

Combine like terms: 7 + -4 = 3
3 + -3x + 24x + 3x2 = 4 + -24x + -4 + 24x

Combine like terms: -3x + 24x = 21x
3 + 21x + 3x2 = 4 + -24x + -4 + 24x

Reorder the terms:
3 + 21x + 3x2 = 4 + -4 + -24x + 24x

Combine like terms: 4 + -4 = 0
3 + 21x + 3x2 = 0 + -24x + 24x
3 + 21x + 3x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
3 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 7x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
1 + 7x + x2 = 0

Solving
1 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 7x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 7x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x + x2 = 0 + -1
7x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
7x + x2 = -1

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -1 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + 7x + x2 = 11.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 3.5 = 3.354101966

Simplifying
x + 3.5 = 3.354101966

Reorder the terms:
3.5 + x = 3.354101966

Solving
3.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.354101966 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.354101966 + -3.5
x = 3.354101966 + -3.5

Combine like terms: 3.354101966 + -3.5 = -0.145898034
x = -0.145898034

Simplifying
x = -0.145898034


Subproblem 2
x + 3.5 = -3.354101966

Simplifying
x + 3.5 = -3.354101966

Reorder the terms:
3.5 + x = -3.354101966

Solving
3.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.354101966 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.354101966 + -3.5
x = -3.354101966 + -3.5

Combine like terms: -3.354101966 + -3.5 = -6.854101966
x = -6.854101966

Simplifying
x = -6.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.145898034, -6.854101966}
Solution
x = {-0.145898034, -6.854101966}

See similar equations:

| 2a-4a=-8 | | 0.2(15)-0.2x+x=0.4(15) | | a/12=7.5 | | v^2-4=-6v | | 20x^2-45x^4=0 | | 4x^2+9y^2+8x-18y+12=0 | | x/7.5=5.7 | | (2.4+9.6)(14-s)=49.6 | | 4y+16x=4 | | -2v-(-10)=14 | | x/45=38 | | 2(56+2)+2c=3(2c+3)+7 | | 6x^2+3=-11x | | 6a^2+7a-5= | | 5(3+3x)=35 | | -4(x+5)=4(x+5) | | 5.6+2.4(s+14)=49.6 | | 9f-7=20 | | (a+3)(8)-(a-5)=(a-1)(a+1)+(a+3)(6) | | -2z-2=2 | | -6(x-2)+5x-5=-9 | | x(7x+5)(3x-1)=0 | | 20Log(x)=-0.5 | | v-5.65=4.7 | | 5(2-3x)(5x+3)=0 | | -2a-5=9 | | -2a-(-10)=0 | | .3x^2-78x+13310=0 | | 2x(x-3)=x(2x+4) | | 3a+20=5a+6 | | 5y+4=29 | | 3(x+4)+3=-15+3x |

Equations solver categories