4x^2+19x-4=0

Simple and best practice solution for 4x^2+19x-4=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+19x-4=0 equation:


Simplifying
4x2 + 19x + -4 = 0

Reorder the terms:
-4 + 19x + 4x2 = 0

Solving
-4 + 19x + 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'.
-1 + 4.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4.75x + x2 = 0 + 1
4.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4.75x + x2 = 1

The x term is 4.75x.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75x + 5.640625 + x2 = 1 + 5.640625

Reorder the terms:
5.640625 + 4.75x + x2 = 1 + 5.640625

Combine like terms: 1 + 5.640625 = 6.640625
5.640625 + 4.75x + x2 = 6.640625

Factor a perfect square on the left side:
(x + 2.375)(x + 2.375) = 6.640625

Calculate the square root of the right side: 2.576941016

Break this problem into two subproblems by setting 
(x + 2.375) equal to 2.576941016 and -2.576941016.

Subproblem 1

x + 2.375 = 2.576941016 Simplifying x + 2.375 = 2.576941016 Reorder the terms: 2.375 + x = 2.576941016 Solving 2.375 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.576941016 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.576941016 + -2.375 x = 2.576941016 + -2.375 Combine like terms: 2.576941016 + -2.375 = 0.201941016 x = 0.201941016 Simplifying x = 0.201941016

Subproblem 2

x + 2.375 = -2.576941016 Simplifying x + 2.375 = -2.576941016 Reorder the terms: 2.375 + x = -2.576941016 Solving 2.375 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.576941016 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.576941016 + -2.375 x = -2.576941016 + -2.375 Combine like terms: -2.576941016 + -2.375 = -4.951941016 x = -4.951941016 Simplifying x = -4.951941016

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.201941016, -4.951941016}

See similar equations:

| 5x-8x=2 | | -4+18=m-8 | | x-9=-5+6 | | -5y=-20+x | | 4y+8=-3x | | 0=-5x-y | | 10=2y+x | | 5y+4=2(y-4) | | -x-6=-5x+22 | | -4x+0=y | | 13-b+4=2-0.5b+6 | | 4y^2+2=(4y+y)+2 | | 7(6x-7)=46 | | 2(2n-1)+6=0 | | 4y^2=(4y*4y)+2 | | 7x-13=-132 | | -3x-7=28 | | -4x=x-1 | | 7x-1=62 | | 10x-9=6c+3 | | 2a^2b^2=0 | | 2a^2xb^2=0 | | -3x+3=8x-85 | | 4y^2+2=4(y+y)+2 | | -14=9y+4 | | 3a^2-4a-7=0 | | 6-2x=-9+3x | | X-(-6)=4 | | 10x+-20=-20 | | 96=2(l+3l)+2w | | -x+1=-31+7x | | 2w+2l=96 |

Equations solver categories