x^2+21x-22=3x-10

Simple and best practice solution for x^2+21x-22=3x-10 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-22=3x-10 equation:


Simplifying
x2 + 21x + -22 = 3x + -10

Reorder the terms:
-22 + 21x + x2 = 3x + -10

Reorder the terms:
-22 + 21x + x2 = -10 + 3x

Solving
-22 + 21x + x2 = -10 + 3x

Solving for variable 'x'.

Reorder the terms:
-22 + 10 + 21x + -3x + x2 = -10 + 3x + 10 + -3x

Combine like terms: -22 + 10 = -12
-12 + 21x + -3x + x2 = -10 + 3x + 10 + -3x

Combine like terms: 21x + -3x = 18x
-12 + 18x + x2 = -10 + 3x + 10 + -3x

Reorder the terms:
-12 + 18x + x2 = -10 + 10 + 3x + -3x

Combine like terms: -10 + 10 = 0
-12 + 18x + x2 = 0 + 3x + -3x
-12 + 18x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 18x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 18x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 18x + x2 = 0 + 12
18x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
18x + x2 = 12

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = 12 + 81

Reorder the terms:
81 + 18x + x2 = 12 + 81

Combine like terms: 12 + 81 = 93
81 + 18x + x2 = 93

Factor a perfect square on the left side:
(x + 9)(x + 9) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(x + 9) equal to 9.643650761 and -9.643650761.

Subproblem 1

x + 9 = 9.643650761 Simplifying x + 9 = 9.643650761 Reorder the terms: 9 + x = 9.643650761 Solving 9 + x = 9.643650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.643650761 + -9 x = 9.643650761 + -9 Combine like terms: 9.643650761 + -9 = 0.643650761 x = 0.643650761 Simplifying x = 0.643650761

Subproblem 2

x + 9 = -9.643650761 Simplifying x + 9 = -9.643650761 Reorder the terms: 9 + x = -9.643650761 Solving 9 + x = -9.643650761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -9.643650761 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.643650761 + -9 x = -9.643650761 + -9 Combine like terms: -9.643650761 + -9 = -18.643650761 x = -18.643650761 Simplifying x = -18.643650761

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.643650761, -18.643650761}

See similar equations:

| 11q-16=6q+4 | | y=-3x^2+12x-20 | | -7(s+-3)+-11=-46 | | x(2x+1)=210 | | 3x^3+9x^2+2x= | | -2t-34+-6t=-10 | | (x+2)(x-2)=96 | | 15x^2=450 | | -7x+6y=9 | | 3-8x+16=9-8x-20 | | 1+6x+9= | | (x-4)(x-4)=64 | | x^2+5x+8=4 | | x^2-10x-30=0 | | 2x+x=45 | | 4x^2-7x=9 | | x+x^2=30 | | 5(x-2)=3(2x+4) | | -4(1+9k)=-8(5k+6) | | p^2-5p=-4 | | 2(w-2+8)+2w=72 | | 3(-7r)-3=3(-5r-12) | | 24=4[k+1]-k | | -45+1.98=27 | | x^2+5x+5=x+1 | | 3x^2-3x-8=2x^2+2 | | 8x^2-9x-14=0 | | x^2+3x-72=4 | | x^2-10x=-2x | | -(.8)y-5=1.5y-2.5 | | x^2-5x+11=11 | | (7x-6)(49x^2-84x+36)=0 |

Equations solver categories