t^2+10t+20=0

Simple and best practice solution for t^2+10t+20=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+10t+20=0 equation:


Simplifying
t2 + 10t + 20 = 0

Reorder the terms:
20 + 10t + t2 = 0

Solving
20 + 10t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 10t + -20 + t2 = 0 + -20

Reorder the terms:
20 + -20 + 10t + t2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 10t + t2 = 0 + -20
10t + t2 = 0 + -20

Combine like terms: 0 + -20 = -20
10t + t2 = -20

The t term is 10t.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10t + 25 + t2 = -20 + 25

Reorder the terms:
25 + 10t + t2 = -20 + 25

Combine like terms: -20 + 25 = 5
25 + 10t + t2 = 5

Factor a perfect square on the left side:
(t + 5)(t + 5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(t + 5) equal to 2.236067978 and -2.236067978.

Subproblem 1

t + 5 = 2.236067978 Simplifying t + 5 = 2.236067978 Reorder the terms: 5 + t = 2.236067978 Solving 5 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + t = 2.236067978 + -5 t = 2.236067978 + -5 Combine like terms: 2.236067978 + -5 = -2.763932022 t = -2.763932022 Simplifying t = -2.763932022

Subproblem 2

t + 5 = -2.236067978 Simplifying t + 5 = -2.236067978 Reorder the terms: 5 + t = -2.236067978 Solving 5 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + t = -2.236067978 + -5 t = -2.236067978 + -5 Combine like terms: -2.236067978 + -5 = -7.236067978 t = -7.236067978 Simplifying t = -7.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-2.763932022, -7.236067978}

See similar equations:

| 4-5p=-34 | | -168=6x+6(5x+8) | | 80-6x=145+7x | | (-4)*(-4)*(-4)= | | x^2-220x+8000=0 | | 14=-4x+6(2x+9) | | 2x+7+9x+8= | | 7-A=21 | | 55=-7x-2(-x-5) | | (-2)3+8(-7)= | | 8r^2-80r+128=0 | | 4-5p=34 | | x^3-6x^2-18x+77=0 | | 4(x+5)=8x+15-4x+5 | | 13v+78=0 | | 6(3x+1)=2x-8x | | (x-y)dy+3dx=0 | | 5a+10=8a+1 | | 18=5e^2x+4 | | (-8)+8= | | 14x+82+5x=8+x | | -5x-2(x+13)=30 | | (x+y)dy-(x-y)dx=0 | | 2ax-4bx+2ay-2ay= | | [1-4]=7 | | 6x-3(5x-2)=87 | | 10-7n=11 | | 3v^2+27v+60=0 | | 2.5y-8y=-10 | | 23+5x=7 | | -63=-3x-3(-6x-9) | | (x-6)(x+8)=8 |

Equations solver categories