45t^2-30t+1=0

Simple and best practice solution for 45t^2-30t+1=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 45t^2-30t+1=0 equation:


Simplifying
45t2 + -30t + 1 = 0

Reorder the terms:
1 + -30t + 45t2 = 0

Solving
1 + -30t + 45t2 = 0

Solving for variable 't'.

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

Divide each side by '45'.
0.02222222222 + -0.6666666667t + t2 = 0

Move the constant term to the right:

Add '-0.02222222222' to each side of the equation.
0.02222222222 + -0.6666666667t + -0.02222222222 + t2 = 0 + -0.02222222222

Reorder the terms:
0.02222222222 + -0.02222222222 + -0.6666666667t + t2 = 0 + -0.02222222222

Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000
0.00000000000 + -0.6666666667t + t2 = 0 + -0.02222222222
-0.6666666667t + t2 = 0 + -0.02222222222

Combine like terms: 0 + -0.02222222222 = -0.02222222222
-0.6666666667t + t2 = -0.02222222222

The t term is -0.6666666667t.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667t + 0.1111111112 + t2 = -0.02222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667t + t2 = -0.02222222222 + 0.1111111112

Combine like terms: -0.02222222222 + 0.1111111112 = 0.08888888898
0.1111111112 + -0.6666666667t + t2 = 0.08888888898

Factor a perfect square on the left side:
(t + -0.3333333334)(t + -0.3333333334) = 0.08888888898

Calculate the square root of the right side: 0.298142397

Break this problem into two subproblems by setting 
(t + -0.3333333334) equal to 0.298142397 and -0.298142397.

Subproblem 1

t + -0.3333333334 = 0.298142397 Simplifying t + -0.3333333334 = 0.298142397 Reorder the terms: -0.3333333334 + t = 0.298142397 Solving -0.3333333334 + t = 0.298142397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + t = 0.298142397 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + t = 0.298142397 + 0.3333333334 t = 0.298142397 + 0.3333333334 Combine like terms: 0.298142397 + 0.3333333334 = 0.6314757304 t = 0.6314757304 Simplifying t = 0.6314757304

Subproblem 2

t + -0.3333333334 = -0.298142397 Simplifying t + -0.3333333334 = -0.298142397 Reorder the terms: -0.3333333334 + t = -0.298142397 Solving -0.3333333334 + t = -0.298142397 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + t = -0.298142397 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + t = -0.298142397 + 0.3333333334 t = -0.298142397 + 0.3333333334 Combine like terms: -0.298142397 + 0.3333333334 = 0.0351909364 t = 0.0351909364 Simplifying t = 0.0351909364

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.6314757304, 0.0351909364}

See similar equations:

| -5x-12+3x-9=-x-7x+12+3x+5 | | 3(a-2)=51 | | 11x+30=2x-42 | | 7(7+19)-19= | | 15x-5=7x+3 | | 15-3x=(-9) | | (x^2)-4ln(x+1)=0 | | -10s-40=-58 | | 5x^2+21x=-4x | | 5x^2+31x=-4x | | 2x+15=-15-2x | | -logx=8.2 | | 8/10:2/3 | | 2x-3+5x=x-1-2x | | -20-8=-m+2m | | 14a=126 | | 25-4h^2= | | 12z+5=0 | | -20-8=m+2m | | x^2+5xy+y^2-123=0 | | 20-8=-m+2m | | 3b+7=0 | | 10x+27=6x+139 | | 2x-2x=-5+3 | | 10x+15=5x+110 | | 2x-3(1-x)= | | (X-4)-4=4x-(4-3x) | | 2(3a+b)-4b= | | 9a-(5a-3b)= | | 3x^2-2ax-2a^2=0 | | 3x=9x+8 | | 7x-14=10x+10 |

Equations solver categories