7t^2-22t+7=0

Simple and best practice solution for 7t^2-22t+7=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 7t^2-22t+7=0 equation:


Simplifying
7t2 + -22t + 7 = 0

Reorder the terms:
7 + -22t + 7t2 = 0

Solving
7 + -22t + 7t2 = 0

Solving for variable 't'.

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

Divide each side by '7'.
1 + -3.142857143t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.142857143t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -3.142857143t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.142857143t + t2 = 0 + -1
-3.142857143t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.142857143t + t2 = -1

The t term is -3.142857143t.  Take half its coefficient (-1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
-3.142857143t + 2.469387757 + t2 = -1 + 2.469387757

Reorder the terms:
2.469387757 + -3.142857143t + t2 = -1 + 2.469387757

Combine like terms: -1 + 2.469387757 = 1.469387757
2.469387757 + -3.142857143t + t2 = 1.469387757

Factor a perfect square on the left side:
(t + -1.571428572)(t + -1.571428572) = 1.469387757

Calculate the square root of the right side: 1.212183054

Break this problem into two subproblems by setting 
(t + -1.571428572) equal to 1.212183054 and -1.212183054.

Subproblem 1

t + -1.571428572 = 1.212183054 Simplifying t + -1.571428572 = 1.212183054 Reorder the terms: -1.571428572 + t = 1.212183054 Solving -1.571428572 + t = 1.212183054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + t = 1.212183054 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + t = 1.212183054 + 1.571428572 t = 1.212183054 + 1.571428572 Combine like terms: 1.212183054 + 1.571428572 = 2.783611626 t = 2.783611626 Simplifying t = 2.783611626

Subproblem 2

t + -1.571428572 = -1.212183054 Simplifying t + -1.571428572 = -1.212183054 Reorder the terms: -1.571428572 + t = -1.212183054 Solving -1.571428572 + t = -1.212183054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.571428572' to each side of the equation. -1.571428572 + 1.571428572 + t = -1.212183054 + 1.571428572 Combine like terms: -1.571428572 + 1.571428572 = 0.000000000 0.000000000 + t = -1.212183054 + 1.571428572 t = -1.212183054 + 1.571428572 Combine like terms: -1.212183054 + 1.571428572 = 0.359245518 t = 0.359245518 Simplifying t = 0.359245518

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.783611626, 0.359245518}

See similar equations:

| (x+20)+3x=90 | | 2x+4(x-3)=12 | | 12=-7+v | | -56-6x-5x=43 | | -16t^2-11t+120=0 | | -16t^2-11t+120=h | | 14+23= | | 0=8-3(6-6x) | | .5y+(2x+5)=180 | | f(3)=12+3x | | s+8=-13.5 | | 4x-6x-7=7 | | 2x+9+7x-4=4x+7 | | 11x-154=-5x+54 | | 3(2y-3)=5(y+4) | | 30+8+7+10+25-4+9+25-3+6-5=108 | | x^2+2x-15=15 | | H+9.7=-9 | | x^3-2x^2-41x-56=0 | | 3xy+2x=4y | | 3(x+5)=6x+15 | | 4x+7=2x+9+7x-4 | | 4.1=d-5.1 | | 3.1x-1.6=5 | | 3=2x+1(x) | | (x)(x)+4x=117 | | 6(a+2b)+8b-16b= | | 5.6+z=3 | | 3x-2=130 | | 7-6y=31-4x | | 6x+6y=224.9 | | 5x+7+2x=4 |

Equations solver categories