2x^2-21x=40

Simple and best practice solution for 2x^2-21x=40 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=40 equation:


Simplifying
2x2 + -21x = 40

Reorder the terms:
-21x + 2x2 = 40

Solving
-21x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + -21x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -21x + 2x2 = 0

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

Divide each side by '2'.
-20 + -10.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -10.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -10.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -10.5x + x2 = 0 + 20
-10.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-10.5x + x2 = 20

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 = 20 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 20 + 27.5625

Combine like terms: 20 + 27.5625 = 47.5625
27.5625 + -10.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + -5.25) equal to 6.896557112 and -6.896557112.

Subproblem 1

x + -5.25 = 6.896557112 Simplifying x + -5.25 = 6.896557112 Reorder the terms: -5.25 + x = 6.896557112 Solving -5.25 + x = 6.896557112 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 = 6.896557112 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 6.896557112 + 5.25 x = 6.896557112 + 5.25 Combine like terms: 6.896557112 + 5.25 = 12.146557112 x = 12.146557112 Simplifying x = 12.146557112

Subproblem 2

x + -5.25 = -6.896557112 Simplifying x + -5.25 = -6.896557112 Reorder the terms: -5.25 + x = -6.896557112 Solving -5.25 + x = -6.896557112 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 = -6.896557112 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -6.896557112 + 5.25 x = -6.896557112 + 5.25 Combine like terms: -6.896557112 + 5.25 = -1.646557112 x = -1.646557112 Simplifying x = -1.646557112

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.146557112, -1.646557112}

See similar equations:

| 2x-5*2+x=54 | | 4/3u-8/5=-3/2 | | -(3+8p)-5p=33-4p | | 9-(2x-9)=3-3x | | 9+19=20 | | (6^8y^-6)/(18xy) | | 4t=60 | | (x+.07x)+.15(x+.07x)=27.00 | | -7x^2+x=8 | | 19(x-15)=180 | | 3p-0.8=4.6 | | 33/x=18/42 | | 8f+f=6 | | log(2x+1)=log(x-3)+(x+5) | | =cos^4x | | (6c^5+7c^2-3)-(9c^5-5c^2+15)= | | 9x^2+x=8 | | 5q-5=20 | | 8x^2-12=-29x | | -1/2(2)-4= | | -3x^2+624x-4800=0 | | 2+ln(x-4)=4 | | -12/3*4/5 | | 5(x-2)+-9=-7(1-x) | | 5+(-3)+(-5)=x | | 3b=3+4(-7+5b) | | 2m-4+m+3=17 | | Y=tan(7x^2) | | 253=5x+3 | | x/93 | | 9w*w=81 | | -3/7*11/12 |

Equations solver categories