2t^2+10t=75

Simple and best practice solution for 2t^2+10t=75 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 2t^2+10t=75 equation:


Simplifying
2t2 + 10t = 75

Reorder the terms:
10t + 2t2 = 75

Solving
10t + 2t2 = 75

Solving for variable 't'.

Reorder the terms:
-75 + 10t + 2t2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 10t + 2t2 = 0

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

Divide each side by '2'.
-37.5 + 5t + t2 = 0

Move the constant term to the right:

Add '37.5' to each side of the equation.
-37.5 + 5t + 37.5 + t2 = 0 + 37.5

Reorder the terms:
-37.5 + 37.5 + 5t + t2 = 0 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + 5t + t2 = 0 + 37.5
5t + t2 = 0 + 37.5

Combine like terms: 0 + 37.5 = 37.5
5t + t2 = 37.5

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = 37.5 + 6.25

Reorder the terms:
6.25 + 5t + t2 = 37.5 + 6.25

Combine like terms: 37.5 + 6.25 = 43.75
6.25 + 5t + t2 = 43.75

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 43.75

Calculate the square root of the right side: 6.614378278

Break this problem into two subproblems by setting 
(t + 2.5) equal to 6.614378278 and -6.614378278.

Subproblem 1

t + 2.5 = 6.614378278 Simplifying t + 2.5 = 6.614378278 Reorder the terms: 2.5 + t = 6.614378278 Solving 2.5 + t = 6.614378278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 6.614378278 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 6.614378278 + -2.5 t = 6.614378278 + -2.5 Combine like terms: 6.614378278 + -2.5 = 4.114378278 t = 4.114378278 Simplifying t = 4.114378278

Subproblem 2

t + 2.5 = -6.614378278 Simplifying t + 2.5 = -6.614378278 Reorder the terms: 2.5 + t = -6.614378278 Solving 2.5 + t = -6.614378278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -6.614378278 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -6.614378278 + -2.5 t = -6.614378278 + -2.5 Combine like terms: -6.614378278 + -2.5 = -9.114378278 t = -9.114378278 Simplifying t = -9.114378278

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.114378278, -9.114378278}

See similar equations:

| 2(3cosx+1)=4cosx | | 14x=5(x-6)+33 | | (6x+7)=90 | | 7+x-15=-2.66667 | | (10/3)x2 | | g=10-1(40) | | y^2-1y-20= | | 10t^2-23t+9=0 | | 30-5(p-10)=16 | | (6x+7)=180 | | -7x^2+6x+288=0 | | 2(x*x-5+2)=0 | | -2(2-3x)=10-x | | 2y+4+6y=-13 | | 0.4x-5=0.5x+7 | | log1/9^(0.67) | | (4x-2)+(x-4)+y=180 | | 7/4m-4/4 | | 2x^2+6x+9=12 | | 4p+3p-10=5+2p | | g=10-P | | 7/4-4/4 | | 8-4n=-15+7 | | G/6-7=-10 | | -1(2x-6)=30 | | 5x+6x+5=-2 | | 2/3x-9-1/3x=5/6 | | 10=2c+4 | | -15a+n=65+(-15a) | | 129=-3(5-6x) | | 2/7=.2(c-1) | | 2/3x-9-1/3=5/6 |

Equations solver categories