x^2+21x=-16

Simple and best practice solution for x^2+21x=-16 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=-16 equation:


Simplifying
x2 + 21x = -16

Reorder the terms:
21x + x2 = -16

Solving
21x + x2 = -16

Solving for variable 'x'.

Reorder the terms:
16 + 21x + x2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 21x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 21x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 21x + x2 = 0 + -16
21x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
21x + x2 = -16

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 = -16 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -16 + 110.25

Combine like terms: -16 + 110.25 = 94.25
110.25 + 21x + x2 = 94.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 94.25

Calculate the square root of the right side: 9.708243919

Break this problem into two subproblems by setting 
(x + 10.5) equal to 9.708243919 and -9.708243919.

Subproblem 1

x + 10.5 = 9.708243919 Simplifying x + 10.5 = 9.708243919 Reorder the terms: 10.5 + x = 9.708243919 Solving 10.5 + x = 9.708243919 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 = 9.708243919 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 9.708243919 + -10.5 x = 9.708243919 + -10.5 Combine like terms: 9.708243919 + -10.5 = -0.791756081 x = -0.791756081 Simplifying x = -0.791756081

Subproblem 2

x + 10.5 = -9.708243919 Simplifying x + 10.5 = -9.708243919 Reorder the terms: 10.5 + x = -9.708243919 Solving 10.5 + x = -9.708243919 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 = -9.708243919 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -9.708243919 + -10.5 x = -9.708243919 + -10.5 Combine like terms: -9.708243919 + -10.5 = -20.208243919 x = -20.208243919 Simplifying x = -20.208243919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.791756081, -20.208243919}

See similar equations:

| x^2+22x=-16 | | x^2+200x=-16 | | 2x+2=15-3 | | 3a+4b+-5a+6b= | | 2x-5=12+6 | | 8p-2(7q-3p)= | | 2+t(3-t)-3t= | | 4a-10-9a+13= | | 5(7-4m)= | | 3x+x(5-x)-8x= | | 3(x+4)=5(x-5) | | 1A+5B=X | | x^2+35x+16=0 | | x^2+25x+16=0 | | x^2+14x+16=0 | | 3x^2y^2+9xy= | | x^2+16x+16=0 | | x^2+15x+16=0 | | 5*a=21 | | x^2+20x+16=0 | | 4*a=52 | | f(x)=x^3-4x^2-7 | | 9x-8+8=3x+19+8 | | 11a=7 | | 4x^2+7x+j=0 | | 6x+22=1x-59 | | 108/x=8 | | 75/x=15 | | 75-x=15 | | 108-x=8 | | 18+x=108 | | 15a-10=5a-40 |

Equations solver categories