4x^2+14x+3=0

Simple and best practice solution for 4x^2+14x+3=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+14x+3=0 equation:


Simplifying
4x2 + 14x + 3 = 0

Reorder the terms:
3 + 14x + 4x2 = 0

Solving
3 + 14x + 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'.
0.75 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 3.5x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 3.5x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 3.5x + x2 = 0 + -0.75
3.5x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
3.5x + x2 = -0.75

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -0.75 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -0.75 + 3.0625

Combine like terms: -0.75 + 3.0625 = 2.3125
3.0625 + 3.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.520690633 and -1.520690633.

Subproblem 1

x + 1.75 = 1.520690633 Simplifying x + 1.75 = 1.520690633 Reorder the terms: 1.75 + x = 1.520690633 Solving 1.75 + x = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.520690633 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.520690633 + -1.75 x = 1.520690633 + -1.75 Combine like terms: 1.520690633 + -1.75 = -0.229309367 x = -0.229309367 Simplifying x = -0.229309367

Subproblem 2

x + 1.75 = -1.520690633 Simplifying x + 1.75 = -1.520690633 Reorder the terms: 1.75 + x = -1.520690633 Solving 1.75 + x = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.520690633 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.520690633 + -1.75 x = -1.520690633 + -1.75 Combine like terms: -1.520690633 + -1.75 = -3.270690633 x = -3.270690633 Simplifying x = -3.270690633

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.229309367, -3.270690633}

See similar equations:

| -19+(-6)= | | 0.7+5.4=-13/5 | | x^3+3x^2-5x-39=0 | | -3(k+6)=-4k-25 | | 4x+60=40 | | 6-x=12x^2 | | 3(4v+1)-3(2v+3)=2(v-7)+w | | 34+4x=-6(1+6x) | | -x+6y=-22 | | x^2=-9x-4 | | x-2(-2)=14 | | n/99=-1 | | 4=3+x | | 4y-9y=10.5 | | 3y-7=-1 | | y=x^2+9x+4 | | .25x+13=.25(2x-32) | | 3/8w-14=10 | | -3(x+3)-1=-2x-5 | | 1/6x+8=17 | | z^6=64i | | 7x-6y=32 | | 7(x^2-7x-7)=67x+2 | | 15/20=x/60 | | n/12=12 | | 3(x+2)+4=x+12 | | x^3-2x^2=2x-1 | | -5(-1+7b)=-32+2b | | x+4(-4x-3)=4x-69 | | 4x^20=0 | | y=x^2+7x-7 | | 3(x+1)+3x=-4x+7 |

Equations solver categories