4t^2+4t-9=0

Simple and best practice solution for 4t^2+4t-9=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 4t^2+4t-9=0 equation:


Simplifying
4t2 + 4t + -9 = 0

Reorder the terms:
-9 + 4t + 4t2 = 0

Solving
-9 + 4t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-2.25 + t + t2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + t + 2.25 + t2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + t + t2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t + t2 = 0 + 2.25
t + t2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
t + t2 = 2.25

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 2.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 2.25 + 0.25

Combine like terms: 2.25 + 0.25 = 2.5
1.25 + t2 = 2.5

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.58113883 and -1.58113883.

Subproblem 1

t + 0.5 = 1.58113883 Simplifying t + 0.5 = 1.58113883 Reorder the terms: 0.5 + t = 1.58113883 Solving 0.5 + t = 1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.58113883 + -0.5 t = 1.58113883 + -0.5 Combine like terms: 1.58113883 + -0.5 = 1.08113883 t = 1.08113883 Simplifying t = 1.08113883

Subproblem 2

t + 0.5 = -1.58113883 Simplifying t + 0.5 = -1.58113883 Reorder the terms: 0.5 + t = -1.58113883 Solving 0.5 + t = -1.58113883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.58113883 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.58113883 + -0.5 t = -1.58113883 + -0.5 Combine like terms: -1.58113883 + -0.5 = -2.08113883 t = -2.08113883 Simplifying t = -2.08113883

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.08113883, -2.08113883}

See similar equations:

| s^2=27-6s | | 2m+4m+8=28 | | 3.4=0.4m-2+0.2m | | -5n-6=5n+4 | | f(x)=3x^3+17x^2-8x-12 | | -4ln(x+3)+8ln(x+5)= | | 20=2p-20 | | 400-15w=1000-40w | | -4lnx+3+8lnx+5= | | Y-(-1)=-2(x-(-9)) | | x-2(4x+2)=-4 | | 1/3b=b/2+8 | | 1000(6x-10)=40(395+100x) | | 6m-4=19 | | 17-x=.333*15+6 | | (6x^3+3x^2-5)+(4x^3-4x-3)= | | x(x+6)(x+9)=0 | | 2(2x+3)=38 | | 3x=7-(x-1) | | 7=2-(5-x)+3 | | 2(8-2x)=16 | | 5(x+6)=55 | | 16-5x=2x+2 | | -2a+14=5a+21 | | 5+12lnx=3 | | -(5y+4)-(-4y-5)=-4 | | -5(v+9)=5v-25 | | 3x^2+8x-40=0 | | -4=3y+5 | | 7-3p+11=-2(6p-9) | | 95+y+y=549 | | 2(a+b)=138 |

Equations solver categories