x^2-21x+69=0

Simple and best practice solution for x^2-21x+69=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 x^2-21x+69=0 equation:


Simplifying
x2 + -21x + 69 = 0

Reorder the terms:
69 + -21x + x2 = 0

Solving
69 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-69' to each side of the equation.
69 + -21x + -69 + x2 = 0 + -69

Reorder the terms:
69 + -69 + -21x + x2 = 0 + -69

Combine like terms: 69 + -69 = 0
0 + -21x + x2 = 0 + -69
-21x + x2 = 0 + -69

Combine like terms: 0 + -69 = -69
-21x + x2 = -69

The x term is -21x.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21x + 110.25 + x2 = -69 + 110.25

Reorder the terms:
110.25 + -21x + x2 = -69 + 110.25

Combine like terms: -69 + 110.25 = 41.25
110.25 + -21x + x2 = 41.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + -10.5) equal to 6.422616289 and -6.422616289.

Subproblem 1

x + -10.5 = 6.422616289 Simplifying x + -10.5 = 6.422616289 Reorder the terms: -10.5 + x = 6.422616289 Solving -10.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 6.422616289 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 6.422616289 + 10.5 x = 6.422616289 + 10.5 Combine like terms: 6.422616289 + 10.5 = 16.922616289 x = 16.922616289 Simplifying x = 16.922616289

Subproblem 2

x + -10.5 = -6.422616289 Simplifying x + -10.5 = -6.422616289 Reorder the terms: -10.5 + x = -6.422616289 Solving -10.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -6.422616289 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -6.422616289 + 10.5 x = -6.422616289 + 10.5 Combine like terms: -6.422616289 + 10.5 = 4.077383711 x = 4.077383711 Simplifying x = 4.077383711

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.922616289, 4.077383711}

See similar equations:

| x^2+10x+87=0 | | 6(7-10x)+3(3-15x)=366 | | 15b^2+25b-40= | | -0.66666666666667x=0.83333333333333 | | -21x^2+95x+6=0 | | 9y+2(6y-5)=53 | | 2x+3c+x+c= | | r(2)-7r+10=0 | | 5x^2-18xy-8y^2= | | (3x)+(x+8)=180 | | 9y+9(14y+2)=288 | | f(x)=6x^2+13x+6 | | 2(x-1)=x-4 | | -8x+5y=7 | | x(2)-x=0 | | 2x^2+3x-7=x^2+5x+39 | | 3(p+9)-12p=51 | | 6-6x+3x=-21 | | 11p=22 | | 5x+10+11x+2+58=360 | | 4x^2+5x=-12 | | 12(m+20)=16m | | x(2)+5x-14=0 | | 8w-30=5w-40 | | 4x^2=-12x-6 | | (x/4)=(x/5)+(7/4) | | 2y-1/21=3y-7/15 | | 10+x+60=90 | | 10=2(2x-1) | | -0.08y+0.10(800-y)=0.07y | | 3x/x+2-x/x-2+8/x^2-4 | | 3x=x+10+2 |

Equations solver categories