45t-16t^2=10

Simple and best practice solution for 45t-16t^2=10 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 45t-16t^2=10 equation:


Simplifying
45t + -16t2 = 10

Solving
45t + -16t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + 45t + -16t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 45t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.625 + -2.8125t + t2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.8125t + -0.625 + t2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.8125t + t2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.8125t + t2 = 0 + -0.625
-2.8125t + t2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.8125t + t2 = -0.625

The t term is -2.8125t.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125t + 1.977539063 + t2 = -0.625 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = -0.625 + 1.977539063

Combine like terms: -0.625 + 1.977539063 = 1.352539063
1.977539063 + -2.8125t + t2 = 1.352539063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 1.352539063

Calculate the square root of the right side: 1.162987129

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 1.162987129 and -1.162987129.

Subproblem 1

t + -1.40625 = 1.162987129 Simplifying t + -1.40625 = 1.162987129 Reorder the terms: -1.40625 + t = 1.162987129 Solving -1.40625 + t = 1.162987129 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.162987129 + 1.40625 t = 1.162987129 + 1.40625 Combine like terms: 1.162987129 + 1.40625 = 2.569237129 t = 2.569237129 Simplifying t = 2.569237129

Subproblem 2

t + -1.40625 = -1.162987129 Simplifying t + -1.40625 = -1.162987129 Reorder the terms: -1.40625 + t = -1.162987129 Solving -1.40625 + t = -1.162987129 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -1.162987129 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.162987129 + 1.40625 t = -1.162987129 + 1.40625 Combine like terms: -1.162987129 + 1.40625 = 0.243262871 t = 0.243262871 Simplifying t = 0.243262871

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.569237129, 0.243262871}

See similar equations:

| 3(4w+5)=1 | | 5x+2{x+14)=-56 | | 1/3x3.14x7^2x12 | | (3x^2+2x-2)-(5x^2-5x+6)= | | 10x-5+4x+3=180 | | a/3=a-2 | | Q=-2P+12 | | 2r^2-4t=1 | | x^2-28y=0 | | 16=1-20n+5 | | 3x-6+2x+16=180 | | g^2+7g+12.5=156.25 | | -32+y=12 | | 5x+2(x+14)=-56 | | 10=-9z+5z+8 | | x-(-1/8)=3/10 | | 4x+13+18x-9+4x+1=180 | | 9p+2=8p+10 | | -9(-7x+8)=-450 | | -7y-5=1-6y | | 27/3-(-44/4) | | 3mn(m-6n)= | | 4y-7=17y+45 | | (x^3-8)/(2x^2-x-6) | | -42/-7 | | -34-10x=57-3x | | x+1=2x-11 | | G+14=6-3g | | 6[9-(3-4)]= | | 4z-6=z+6 | | 2m=3+1 | | -12-16k=6(1+4k) |

Equations solver categories