t^2+8t+16=45

Simple and best practice solution for t^2+8t+16=45 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 t^2+8t+16=45 equation:


Simplifying
t2 + 8t + 16 = 45

Reorder the terms:
16 + 8t + t2 = 45

Solving
16 + 8t + t2 = 45

Solving for variable 't'.

Reorder the terms:
16 + -45 + 8t + t2 = 45 + -45

Combine like terms: 16 + -45 = -29
-29 + 8t + t2 = 45 + -45

Combine like terms: 45 + -45 = 0
-29 + 8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 8t + 29 + t2 = 0 + 29

Reorder the terms:
-29 + 29 + 8t + t2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 8t + t2 = 0 + 29
8t + t2 = 0 + 29

Combine like terms: 0 + 29 = 29
8t + t2 = 29

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 29 + 16

Reorder the terms:
16 + 8t + t2 = 29 + 16

Combine like terms: 29 + 16 = 45
16 + 8t + t2 = 45

Factor a perfect square on the left side:
(t + 4)(t + 4) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(t + 4) equal to 6.708203933 and -6.708203933.

Subproblem 1

t + 4 = 6.708203933 Simplifying t + 4 = 6.708203933 Reorder the terms: 4 + t = 6.708203933 Solving 4 + t = 6.708203933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + t = 6.708203933 + -4 t = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 t = 2.708203933 Simplifying t = 2.708203933

Subproblem 2

t + 4 = -6.708203933 Simplifying t + 4 = -6.708203933 Reorder the terms: 4 + t = -6.708203933 Solving 4 + t = -6.708203933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + t = -6.708203933 + -4 t = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 t = -10.708203933 Simplifying t = -10.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.708203933, -10.708203933}

See similar equations:

| 12x(a-b)+(c+d)3= | | 8x=4(6x+12) | | x^4-10x^2=9 | | 2x+32=12x-88 | | 2(x-3)+6=22 | | 5a-(3a+2a)= | | x^2-22x+121=13 | | 6x^3-2x^2-8x=0 | | 4x^3-12x^2-x+3=0 | | 12x-14=107 | | m^2-2+1=144 | | 5x+6+6x-4= | | 14-y-5=3y+27-10 | | 8x-2(6-x)=13 | | 5(5x-3)+13=-1 | | -(6x-5y+7)= | | 2x+3.2=9.4 | | 3x+3=(x-7) | | -6x+25=-23 | | 11(x-7)=-6-5 | | 5-3(3x+1)=4x+(x-8) | | -3(4n+3)=18 | | 3(2y-1)=y | | 7x-18=-40 | | 2x-3y=13 | | x+18+x+9=x-3 | | 2r^2+4r-232=0 | | v^2+2v-24=0 | | 5x-10.2=3x-11 | | 0.3x+0.2=-0.4 | | 3x-10=x+30 | | 4(3x+1)+30=8x-2 |

Equations solver categories