7t^2-20t=13

Simple and best practice solution for 7t^2-20t=13 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^2-20t=13 equation:


Simplifying
7t2 + -20t = 13

Reorder the terms:
-20t + 7t2 = 13

Solving
-20t + 7t2 = 13

Solving for variable 't'.

Reorder the terms:
-13 + -20t + 7t2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -20t + 7t2 = 0

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

Divide each side by '7'.
-1.857142857 + -2.857142857t + t2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + -2.857142857t + 1.857142857 + t2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + -2.857142857t + t2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + -2.857142857t + t2 = 0 + 1.857142857
-2.857142857t + t2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
-2.857142857t + t2 = 1.857142857

The t term is -2.857142857t.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857t + 2.040816328 + t2 = 1.857142857 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857t + t2 = 1.857142857 + 2.040816328

Combine like terms: 1.857142857 + 2.040816328 = 3.897959185
2.040816328 + -2.857142857t + t2 = 3.897959185

Factor a perfect square on the left side:
(t + -1.428571429)(t + -1.428571429) = 3.897959185

Calculate the square root of the right side: 1.974324995

Break this problem into two subproblems by setting 
(t + -1.428571429) equal to 1.974324995 and -1.974324995.

Subproblem 1

t + -1.428571429 = 1.974324995 Simplifying t + -1.428571429 = 1.974324995 Reorder the terms: -1.428571429 + t = 1.974324995 Solving -1.428571429 + t = 1.974324995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 1.974324995 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 1.974324995 + 1.428571429 t = 1.974324995 + 1.428571429 Combine like terms: 1.974324995 + 1.428571429 = 3.402896424 t = 3.402896424 Simplifying t = 3.402896424

Subproblem 2

t + -1.428571429 = -1.974324995 Simplifying t + -1.428571429 = -1.974324995 Reorder the terms: -1.428571429 + t = -1.974324995 Solving -1.428571429 + t = -1.974324995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -1.974324995 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -1.974324995 + 1.428571429 t = -1.974324995 + 1.428571429 Combine like terms: -1.974324995 + 1.428571429 = -0.545753566 t = -0.545753566 Simplifying t = -0.545753566

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.402896424, -0.545753566}

See similar equations:

| x=3+4y | | 2x-8=y | | -2v-3=25 | | 2s^2-5=9s | | 10f-12=38 | | 2x^2-6x=36 | | -12x+12=-24 | | 1-1-3=0 | | x^2+3=3x | | 2(x+1)=-6 | | 2r^2-9=2r | | -12s-11=1s+4 | | 4x-3(x+5)=10 | | -6b-20=40 | | 3z^2+5=14z | | 3m^2+22m+35=0 | | 5n^2-54n+40=0 | | 4[x-2]=x+1 | | Y^2+6y=6 | | 25x^2+5x-2=0 | | 9x+14=41 | | -2[x-6]=4 | | 5x+5=x+6 | | 3[2-5x]=-9 | | (p-4)(p-2)=0 | | b(7b+8)=0 | | 2[3x+4]=8 | | 7z^2-8z-1=0 | | 8x^5=-1000x^2 | | 3-4(t+1)=7 | | 4x^2-3x-22=0 | | 48y^3=3Y |

Equations solver categories