4x^2-24x+21=0

Simple and best practice solution for 4x^2-24x+21=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 4x^2-24x+21=0 equation:


Simplifying
4x2 + -24x + 21 = 0

Reorder the terms:
21 + -24x + 4x2 = 0

Solving
21 + -24x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
5.25 + -6x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -6x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -6x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -6x + x2 = 0 + -5.25
-6x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-6x + x2 = -5.25

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -5.25 + 9

Reorder the terms:
9 + -6x + x2 = -5.25 + 9

Combine like terms: -5.25 + 9 = 3.75
9 + -6x + x2 = 3.75

Factor a perfect square on the left side:
(x + -3)(x + -3) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(x + -3) equal to 1.936491673 and -1.936491673.

Subproblem 1

x + -3 = 1.936491673 Simplifying x + -3 = 1.936491673 Reorder the terms: -3 + x = 1.936491673 Solving -3 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.936491673 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.936491673 + 3 x = 1.936491673 + 3 Combine like terms: 1.936491673 + 3 = 4.936491673 x = 4.936491673 Simplifying x = 4.936491673

Subproblem 2

x + -3 = -1.936491673 Simplifying x + -3 = -1.936491673 Reorder the terms: -3 + x = -1.936491673 Solving -3 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.936491673 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.936491673 + 3 x = -1.936491673 + 3 Combine like terms: -1.936491673 + 3 = 1.063508327 x = 1.063508327 Simplifying x = 1.063508327

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.936491673, 1.063508327}

See similar equations:

| x+(x*0.07)=3103 | | x^2-3x=10.71 | | 7.6=d-5.2 | | 154=37x-14+19x | | 3/4x^2-48=0 | | -25=9 | | 15p=135 | | 18xy=1 | | k^2+9=58 | | 3.5X=(10-b)X | | 152=31+11x | | -5(m+6)-3m=-94 | | 3s=7/9 | | 7n=53+35 | | 12Z+2=5Z-19 | | 11x^2-6000x-27500=0 | | 6(x-2)=9(x-3) | | 7.80+.65y=6.80+.90x | | 0=8x^3+34x^2-29x+5 | | 2x^3+x-8=0 | | -90=-38+4x | | (6x^6/y)^-3 | | -90=-38+4 | | 46*49=56x | | Y=2.3-1.8 | | 46*49=x | | -112=-4(7-3n) | | 2(y-5)=-10y | | 13-5=52 | | a^2-56=-a | | (x+y)(b+x)=0 | | 6(2x+5)+8=12x+38 |

Equations solver categories