4x^2+33x+61=0

Simple and best practice solution for 4x^2+33x+61=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 4x^2+33x+61=0 equation:


Simplifying
4x2 + 33x + 61 = 0

Reorder the terms:
61 + 33x + 4x2 = 0

Solving
61 + 33x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
15.25 + 8.25x + x2 = 0

Move the constant term to the right:

Add '-15.25' to each side of the equation.
15.25 + 8.25x + -15.25 + x2 = 0 + -15.25

Reorder the terms:
15.25 + -15.25 + 8.25x + x2 = 0 + -15.25

Combine like terms: 15.25 + -15.25 = 0.00
0.00 + 8.25x + x2 = 0 + -15.25
8.25x + x2 = 0 + -15.25

Combine like terms: 0 + -15.25 = -15.25
8.25x + x2 = -15.25

The x term is 8.25x.  Take half its coefficient (4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
8.25x + 17.015625 + x2 = -15.25 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = -15.25 + 17.015625

Combine like terms: -15.25 + 17.015625 = 1.765625
17.015625 + 8.25x + x2 = 1.765625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + 4.125) equal to 1.328768227 and -1.328768227.

Subproblem 1

x + 4.125 = 1.328768227 Simplifying x + 4.125 = 1.328768227 Reorder the terms: 4.125 + x = 1.328768227 Solving 4.125 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = 1.328768227 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = 1.328768227 + -4.125 x = 1.328768227 + -4.125 Combine like terms: 1.328768227 + -4.125 = -2.796231773 x = -2.796231773 Simplifying x = -2.796231773

Subproblem 2

x + 4.125 = -1.328768227 Simplifying x + 4.125 = -1.328768227 Reorder the terms: 4.125 + x = -1.328768227 Solving 4.125 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.125' to each side of the equation. 4.125 + -4.125 + x = -1.328768227 + -4.125 Combine like terms: 4.125 + -4.125 = 0.000 0.000 + x = -1.328768227 + -4.125 x = -1.328768227 + -4.125 Combine like terms: -1.328768227 + -4.125 = -5.453768227 x = -5.453768227 Simplifying x = -5.453768227

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.796231773, -5.453768227}

See similar equations:

| x-(-6)=-72 | | .10x+.05(8-x)=.10(12) | | 3(2+v)-4v=v+6 | | 1.7x+0.9=2x | | 25=5(5t+1) | | 20x+2x= | | x-(-36)=39 | | (-3i)(4i)(-5i)= | | 2x+10y=-100 | | .5-6m=.1m-4 | | .90x+.5(18-x)=.10(-144) | | 2x+10y=100 | | x-(-32)=4 | | 2-7x^2=6x+3 | | 0.5-6m=0.1-4 | | 3(2d+1)=9 | | 3x-10=5+9 | | 36+x=70 | | 36+x=30 | | 107-5x=31x+15 | | 1.2x-7=6x-16.6 | | n+2=206 | | .4x+.16(20-x)=20(.22) | | 7=3y-3-(y-2) | | z=9x+12y | | 1-2(x-4)+1=2/3+4 | | 5-3(2x-1)=4x-22 | | n+1=57 | | 5+17=23 | | x+5x+(5x+4)=99 | | 1000x+200=640 | | 1.5(4z+0.25)=2(z+0.0625) |

Equations solver categories