780=4t^2+7t+600

Simple and best practice solution for 780=4t^2+7t+600 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 780=4t^2+7t+600 equation:


Simplifying
780 = 4t2 + 7t + 600

Reorder the terms:
780 = 600 + 7t + 4t2

Solving
780 = 600 + 7t + 4t2

Solving for variable 't'.

Combine like terms: 780 + -600 = 180
180 + -7t + -4t2 = 600 + 7t + 4t2 + -600 + -7t + -4t2

Reorder the terms:
180 + -7t + -4t2 = 600 + -600 + 7t + -7t + 4t2 + -4t2

Combine like terms: 600 + -600 = 0
180 + -7t + -4t2 = 0 + 7t + -7t + 4t2 + -4t2
180 + -7t + -4t2 = 7t + -7t + 4t2 + -4t2

Combine like terms: 7t + -7t = 0
180 + -7t + -4t2 = 0 + 4t2 + -4t2
180 + -7t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
180 + -7t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-45 + 1.75t + t2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 1.75t + 45 + t2 = 0 + 45

Reorder the terms:
-45 + 45 + 1.75t + t2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 1.75t + t2 = 0 + 45
1.75t + t2 = 0 + 45

Combine like terms: 0 + 45 = 45
1.75t + t2 = 45

The t term is 1.75t.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75t + 0.765625 + t2 = 45 + 0.765625

Reorder the terms:
0.765625 + 1.75t + t2 = 45 + 0.765625

Combine like terms: 45 + 0.765625 = 45.765625
0.765625 + 1.75t + t2 = 45.765625

Factor a perfect square on the left side:
(t + 0.875)(t + 0.875) = 45.765625

Calculate the square root of the right side: 6.765029564

Break this problem into two subproblems by setting 
(t + 0.875) equal to 6.765029564 and -6.765029564.

Subproblem 1

t + 0.875 = 6.765029564 Simplifying t + 0.875 = 6.765029564 Reorder the terms: 0.875 + t = 6.765029564 Solving 0.875 + t = 6.765029564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + t = 6.765029564 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + t = 6.765029564 + -0.875 t = 6.765029564 + -0.875 Combine like terms: 6.765029564 + -0.875 = 5.890029564 t = 5.890029564 Simplifying t = 5.890029564

Subproblem 2

t + 0.875 = -6.765029564 Simplifying t + 0.875 = -6.765029564 Reorder the terms: 0.875 + t = -6.765029564 Solving 0.875 + t = -6.765029564 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + t = -6.765029564 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + t = -6.765029564 + -0.875 t = -6.765029564 + -0.875 Combine like terms: -6.765029564 + -0.875 = -7.640029564 t = -7.640029564 Simplifying t = -7.640029564

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.890029564, -7.640029564}

See similar equations:

| 63=x-.23x | | -4(3u-8)+2u=2(u+8) | | 49*2=3a-1a | | (9-d)*11=55 | | 4(3b-5)+2=-114 | | 5t=14 | | x^2=64forx | | 1/2(108+f)=73 | | 6m-27+18m=-10m+29 | | (49/100)-x^2=0 | | 8x+1=162 | | 6k^2+5k-4=0 | | (49/100)-x=0 | | 0=-lnx | | (4y+5)(y+3)=-4(4y+5) | | y=-1+(1-lnx) | | 15x-9=40x+1 | | 24x^2+2x=35 | | 5/6x+18+1/6x=6-3(x-4) | | (6+w)(3w-5)=0 | | 5x+1=7x-(3) | | y=18/-6 | | 175000.00+550x=35000.00+1680.00x | | 2x+18=116 | | y=1/2x+9 | | -7d+3=-3d+11 | | x-5/100x+2/3*5/100x=59 | | 0.5(6p-8)=17 | | 4(r-4)=-10 | | log(5)(2x+5)=1 | | 102-6x=12x+24 | | -42/3=2n/3 |

Equations solver categories