-t^2+31t+145=0

Simple and best practice solution for -t^2+31t+145=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 -t^2+31t+145=0 equation:


Simplifying
-1t2 + 31t + 145 = 0

Reorder the terms:
145 + 31t + -1t2 = 0

Solving
145 + 31t + -1t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-145 + -31t + t2 = 0

Move the constant term to the right:

Add '145' to each side of the equation.
-145 + -31t + 145 + t2 = 0 + 145

Reorder the terms:
-145 + 145 + -31t + t2 = 0 + 145

Combine like terms: -145 + 145 = 0
0 + -31t + t2 = 0 + 145
-31t + t2 = 0 + 145

Combine like terms: 0 + 145 = 145
-31t + t2 = 145

The t term is -31t.  Take half its coefficient (-15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
-31t + 240.25 + t2 = 145 + 240.25

Reorder the terms:
240.25 + -31t + t2 = 145 + 240.25

Combine like terms: 145 + 240.25 = 385.25
240.25 + -31t + t2 = 385.25

Factor a perfect square on the left side:
(t + -15.5)(t + -15.5) = 385.25

Calculate the square root of the right side: 19.627786426

Break this problem into two subproblems by setting 
(t + -15.5) equal to 19.627786426 and -19.627786426.

Subproblem 1

t + -15.5 = 19.627786426 Simplifying t + -15.5 = 19.627786426 Reorder the terms: -15.5 + t = 19.627786426 Solving -15.5 + t = 19.627786426 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = 19.627786426 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = 19.627786426 + 15.5 t = 19.627786426 + 15.5 Combine like terms: 19.627786426 + 15.5 = 35.127786426 t = 35.127786426 Simplifying t = 35.127786426

Subproblem 2

t + -15.5 = -19.627786426 Simplifying t + -15.5 = -19.627786426 Reorder the terms: -15.5 + t = -19.627786426 Solving -15.5 + t = -19.627786426 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = -19.627786426 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = -19.627786426 + 15.5 t = -19.627786426 + 15.5 Combine like terms: -19.627786426 + 15.5 = -4.127786426 t = -4.127786426 Simplifying t = -4.127786426

Solution

The solution to the problem is based on the solutions from the subproblems. t = {35.127786426, -4.127786426}

See similar equations:

| 12xq^2+34xq-28x= | | 10(v+1)-4v=3(2v+1)-11 | | 1y^2-4x=0 | | 2b^2-20b=0 | | 7x-6y=11fory | | 1x^2-9x+8=0 | | -66=6x | | 5*ln(x)=15 | | 5ln(x)=15 | | 4(x+2)-6=12 | | 6p^2-23p=4 | | 60x+120y=2400 | | 1x+15=5x-9 | | 5y-9=4y+2 | | 6m/n^2 | | x=4-(-2) | | 2x^2-56x=-7x^2-3x-40 | | 32^(-4/5) | | 35x-35y=-35 | | 4x^2+8x-18=22-19x | | -1=-5c+11 | | 40x^2-53x+9=0 | | 4x-22=3x-10 | | -49x^2+35-6=0 | | 2y-6=3y-10 | | 9/10=x/8 | | 4x-22=x-2 | | -8.24+3.7= | | 32t^3-16t^2+200=0 | | 6/10*10 | | -4/9y=-16 | | (-2)+p=4 |

Equations solver categories