4t^2-28t=49

Simple and best practice solution for 4t^2-28t=49 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 4t^2-28t=49 equation:


Simplifying
4t2 + -28t = 49

Reorder the terms:
-28t + 4t2 = 49

Solving
-28t + 4t2 = 49

Solving for variable 't'.

Reorder the terms:
-49 + -28t + 4t2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + -28t + 4t2 = 0

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

Divide each side by '4'.
-12.25 + -7t + t2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + -7t + 12.25 + t2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + -7t + t2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + -7t + t2 = 0 + 12.25
-7t + t2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
-7t + t2 = 12.25

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 12.25 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 12.25 + 12.25

Combine like terms: 12.25 + 12.25 = 24.5
12.25 + -7t + t2 = 24.5

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 24.5

Calculate the square root of the right side: 4.949747468

Break this problem into two subproblems by setting 
(t + -3.5) equal to 4.949747468 and -4.949747468.

Subproblem 1

t + -3.5 = 4.949747468 Simplifying t + -3.5 = 4.949747468 Reorder the terms: -3.5 + t = 4.949747468 Solving -3.5 + t = 4.949747468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 4.949747468 + 3.5 t = 4.949747468 + 3.5 Combine like terms: 4.949747468 + 3.5 = 8.449747468 t = 8.449747468 Simplifying t = 8.449747468

Subproblem 2

t + -3.5 = -4.949747468 Simplifying t + -3.5 = -4.949747468 Reorder the terms: -3.5 + t = -4.949747468 Solving -3.5 + t = -4.949747468 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -4.949747468 + 3.5 t = -4.949747468 + 3.5 Combine like terms: -4.949747468 + 3.5 = -1.449747468 t = -1.449747468 Simplifying t = -1.449747468

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.449747468, -1.449747468}

See similar equations:

| 6=n+3(n-2) | | x^2-4y+2y^2=0 | | 8x-2=15x-4x | | 9-4(2x-3)=2(x+1) | | 23=62-e | | 2r+-7=-1 | | c-75=7 | | m+7=-115 | | 6y-2[7(y+1)+4]=10y | | 5d+9-4d=51 | | -5(2w+1)-w=39 | | 13-21=-8 | | 8x+3=4+5x+13 | | B+1-3b=2(3b-3)-7b | | (3x+2)+(x-7)-(2x+5)= | | 3+5z+x^2=0 | | 6x+28-20=6x | | 4x-7y=32 | | 5(m+4)-7(m+2)=-4 | | 39=x+1+3x | | 5-2x=2x-5 | | 6n+3(5n-4)=12(2n-5) | | 9p+p=11+8p | | Y=X+55000 | | 92=x+2-1 | | 24(x+3)=6(4x+1)+66 | | 18x-6y=-24 | | -36=6(2-3m) | | 1.1+x=-5.3 | | 2xwhat=120 | | (x+y^2)dy+(y-x^2)dx=0 | | (6x+7)+x(8x-3)+7x+2m+8x= |

Equations solver categories