z^2-24z=-49

Simple and best practice solution for z^2-24z=-49 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 z^2-24z=-49 equation:


Simplifying
z2 + -24z = -49

Reorder the terms:
-24z + z2 = -49

Solving
-24z + z2 = -49

Solving for variable 'z'.

Reorder the terms:
49 + -24z + z2 = -49 + 49

Combine like terms: -49 + 49 = 0
49 + -24z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + -24z + -49 + z2 = 0 + -49

Reorder the terms:
49 + -49 + -24z + z2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -24z + z2 = 0 + -49
-24z + z2 = 0 + -49

Combine like terms: 0 + -49 = -49
-24z + z2 = -49

The z term is -24z.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24z + 144 + z2 = -49 + 144

Reorder the terms:
144 + -24z + z2 = -49 + 144

Combine like terms: -49 + 144 = 95
144 + -24z + z2 = 95

Factor a perfect square on the left side:
(z + -12)(z + -12) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(z + -12) equal to 9.746794345 and -9.746794345.

Subproblem 1

z + -12 = 9.746794345 Simplifying z + -12 = 9.746794345 Reorder the terms: -12 + z = 9.746794345 Solving -12 + z = 9.746794345 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + z = 9.746794345 + 12 Combine like terms: -12 + 12 = 0 0 + z = 9.746794345 + 12 z = 9.746794345 + 12 Combine like terms: 9.746794345 + 12 = 21.746794345 z = 21.746794345 Simplifying z = 21.746794345

Subproblem 2

z + -12 = -9.746794345 Simplifying z + -12 = -9.746794345 Reorder the terms: -12 + z = -9.746794345 Solving -12 + z = -9.746794345 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + z = -9.746794345 + 12 Combine like terms: -12 + 12 = 0 0 + z = -9.746794345 + 12 z = -9.746794345 + 12 Combine like terms: -9.746794345 + 12 = 2.253205655 z = 2.253205655 Simplifying z = 2.253205655

Solution

The solution to the problem is based on the solutions from the subproblems. z = {21.746794345, 2.253205655}

See similar equations:

| r-5=30 | | (0.1x-1/100)(0.01x-1/10)=0 | | 0.0105263b=26 | | 3x*2x=45 | | 6+3b-5a-5b= | | (3m-7)(4m+5)=0 | | x(-6x+6)=0 | | 5/4ths(a-8)=2/3rds | | c+210=-8c+3 | | r^2-6r-37=0 | | x+1.7x+1.3x= | | 7+8r-2=9r+29-4r | | 2y+3x+2y+3x=21 | | 7t-11=17 | | X+2(7)=12 | | 6x-2y=66 | | ((14/x^3)*-x | | 6x^2+42x+3=3 | | 2x+2+x+3=180 | | (3/4y-1/4)(1/2y-3/20)=0 | | 35=(x-8)+17 | | x/-4-4=4 | | (3/4y-1/4)(1/2y-3/20=0 | | b=1/2jp | | 1/95xb=27170/1045 | | d^2-30d+7=0 | | 6(x-10)=-48 | | 11y=1-4x | | 1/3(9x-3)-3=4-x | | f^2+10f=-1 | | 9+5k=49 | | 7a+10b-6a-8b= |

Equations solver categories