4x^2+28x+1=0

Simple and best practice solution for 4x^2+28x+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 4x^2+28x+1=0 equation:


Simplifying
4x2 + 28x + 1 = 0

Reorder the terms:
1 + 28x + 4x2 = 0

Solving
1 + 28x + 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'.
0.25 + 7x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 7x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 7x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 7x + x2 = 0 + -0.25
7x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
7x + x2 = -0.25

The x term is 7x.  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.
7x + 12.25 + x2 = -0.25 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -0.25 + 12.25

Combine like terms: -0.25 + 12.25 = 12
12.25 + 7x + x2 = 12

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 3.5 = 3.464101615 Simplifying x + 3.5 = 3.464101615 Reorder the terms: 3.5 + x = 3.464101615 Solving 3.5 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.464101615 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.464101615 + -3.5 x = 3.464101615 + -3.5 Combine like terms: 3.464101615 + -3.5 = -0.035898385 x = -0.035898385 Simplifying x = -0.035898385

Subproblem 2

x + 3.5 = -3.464101615 Simplifying x + 3.5 = -3.464101615 Reorder the terms: 3.5 + x = -3.464101615 Solving 3.5 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.464101615 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.464101615 + -3.5 x = -3.464101615 + -3.5 Combine like terms: -3.464101615 + -3.5 = -6.964101615 x = -6.964101615 Simplifying x = -6.964101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.035898385, -6.964101615}

See similar equations:

| 3(1-x)=2(1+x) | | Y=5x+18z | | x^3-3x^2y=c | | 11r+15+2r^2=0 | | 4x^2+2x+1=25 | | 3x(162x)-(162X)3X= | | x^2+4=y | | y^11-7y^1+12y=0 | | (4x-6)=2x+1 | | x+7-4x=19-28 | | -x^2+130x-2000=0 | | 2(3x-7)=4x-3(2-2x) | | 1.9+0.2x=0.5x-3.2 | | -6+8x+7=x-41 | | 41x^2-502x+2136=0 | | 3(2x-7)-5x=5 | | r-11/9=52/3 | | Y=-5/4x-3/4 | | 60=0.12x+82.57 | | 8(2x-5)-15x=8 | | -0.8x^2+120x=0 | | 7x+7+3x= | | 75000000x+455541545x^3+5565689865x^7=0 | | 22-9(3+x)+x= | | 1/12(x-4y-3z) | | 2w-5=1 | | 2n+8=22 | | 2c-3=-5 | | 2d+5=5 | | 7+(3*5)-1= | | 5(3y-8)-(8y-5)= | | 4z-12=12 |

Equations solver categories