2x^2-21x+7=0

Simple and best practice solution for 2x^2-21x+7=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 2x^2-21x+7=0 equation:


Simplifying
2x2 + -21x + 7 = 0

Reorder the terms:
7 + -21x + 2x2 = 0

Solving
7 + -21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
3.5 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -10.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -10.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -10.5x + x2 = 0 + -3.5
-10.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-10.5x + x2 = -3.5

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -3.5 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -3.5 + 27.5625

Combine like terms: -3.5 + 27.5625 = 24.0625
27.5625 + -10.5x + x2 = 24.0625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 24.0625

Calculate the square root of the right side: 4.905354218

Break this problem into two subproblems by setting 
(x + -5.25) equal to 4.905354218 and -4.905354218.

Subproblem 1

x + -5.25 = 4.905354218 Simplifying x + -5.25 = 4.905354218 Reorder the terms: -5.25 + x = 4.905354218 Solving -5.25 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.905354218 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.905354218 + 5.25 x = 4.905354218 + 5.25 Combine like terms: 4.905354218 + 5.25 = 10.155354218 x = 10.155354218 Simplifying x = 10.155354218

Subproblem 2

x + -5.25 = -4.905354218 Simplifying x + -5.25 = -4.905354218 Reorder the terms: -5.25 + x = -4.905354218 Solving -5.25 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.905354218 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.905354218 + 5.25 x = -4.905354218 + 5.25 Combine like terms: -4.905354218 + 5.25 = 0.344645782 x = 0.344645782 Simplifying x = 0.344645782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.155354218, 0.344645782}

See similar equations:

| (5a-2)(6a-5)= | | 5d+4d+d-9d-1=6 | | -8x+32=-24 | | 7n-4n=3n | | x+(x*.169)=10000 | | x+(x*169)=10000 | | -2x-2=17.6 | | -2x-4=17 | | 5a-9=41 | | 10n=.025 | | w/24=8 | | 3x-(4)=2x+(1) | | x+(x*1.169)=10000 | | 0.04x=20 | | 6+x=9+x-x | | 5(3-x)-4=18 | | 4.5/x=3 | | n+2-5/25-5=2n+1/5 | | 112,06=x+62,3/4 | | 12=-1/3t | | 0.3/x=1.5 | | 7+ab-a= | | x+3x-5/6-5=3x+4/3 | | 112,06=x+623/4 | | -2(2x-9)=-22 | | 10x+3=4x-21 | | 29+x=6 | | x=3x/8 | | 2y^2+2y^3= | | 6x^2-30x+5=0 | | -5(-2x-1)=-37 | | 4(x+9)=10 |

Equations solver categories