4t^2-4t-45=0

Simple and best practice solution for 4t^2-4t-45=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 4t^2-4t-45=0 equation:


Simplifying
4t2 + -4t + -45 = 0

Reorder the terms:
-45 + -4t + 4t2 = 0

Solving
-45 + -4t + 4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-11.25 + -1t + t2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -1t + 11.25 + t2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -1t + t2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -1t + t2 = 0 + 11.25
-1t + t2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-1t + t2 = 11.25

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 11.25 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 11.25 + 0.25

Combine like terms: 11.25 + 0.25 = 11.5
0.25 + -1t + t2 = 11.5

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(t + -0.5) equal to 3.391164992 and -3.391164992.

Subproblem 1

t + -0.5 = 3.391164992 Simplifying t + -0.5 = 3.391164992 Reorder the terms: -0.5 + t = 3.391164992 Solving -0.5 + t = 3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 3.391164992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 3.391164992 + 0.5 t = 3.391164992 + 0.5 Combine like terms: 3.391164992 + 0.5 = 3.891164992 t = 3.891164992 Simplifying t = 3.891164992

Subproblem 2

t + -0.5 = -3.391164992 Simplifying t + -0.5 = -3.391164992 Reorder the terms: -0.5 + t = -3.391164992 Solving -0.5 + t = -3.391164992 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -3.391164992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -3.391164992 + 0.5 t = -3.391164992 + 0.5 Combine like terms: -3.391164992 + 0.5 = -2.891164992 t = -2.891164992 Simplifying t = -2.891164992

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.891164992, -2.891164992}

See similar equations:

| 19.3-c=4.507 | | 7p+6=15+6p | | x+3-2x=4 | | x/2=-5(-2) | | 6f+2=4f+11 | | 121-2x=21 | | 11+6y=10y-9 | | 2(2x-5)=34 | | 7x(-2)=10 | | 7x+3=10x | | 556/16=x | | -x^2+2x=-42 | | r^3+r^2+r-1=0 | | 5n+10=4 | | 4x+3(2-x)=3(4-x)-5 | | 12-9x=100-37x | | 8d=0.3 | | 230=12+9.25 | | z^4+81=0 | | 4x+7y+5x-y= | | 5n+10=8 | | 6x-5y=35 | | (3x-7)+(4x-1)=180 | | 6x=5y+35 | | 5n+10=6 | | 4(x-4)+1=6x-2(5+x) | | 5n+12=5 | | 5y^2+3y+4=0 | | 225+225=1x | | 2x+3/5=2-x/3-x | | 5x-0=25 | | 3x-5y=36 |

Equations solver categories