4x^2+20x-19=0

Simple and best practice solution for 4x^2+20x-19=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+20x-19=0 equation:


Simplifying
4x2 + 20x + -19 = 0

Reorder the terms:
-19 + 20x + 4x2 = 0

Solving
-19 + 20x + 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'.
-4.75 + 5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 5x + x2 = 0 + 4.75
5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
5x + x2 = 4.75

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 4.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 4.75 + 6.25

Combine like terms: 4.75 + 6.25 = 11
6.25 + 5x + x2 = 11

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + 2.5 = 3.31662479 Simplifying x + 2.5 = 3.31662479 Reorder the terms: 2.5 + x = 3.31662479 Solving 2.5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.31662479 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.31662479 + -2.5 x = 3.31662479 + -2.5 Combine like terms: 3.31662479 + -2.5 = 0.81662479 x = 0.81662479 Simplifying x = 0.81662479

Subproblem 2

x + 2.5 = -3.31662479 Simplifying x + 2.5 = -3.31662479 Reorder the terms: 2.5 + x = -3.31662479 Solving 2.5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.31662479 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.31662479 + -2.5 x = -3.31662479 + -2.5 Combine like terms: -3.31662479 + -2.5 = -5.81662479 x = -5.81662479 Simplifying x = -5.81662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.81662479, -5.81662479}

See similar equations:

| 23=-4-3x | | 6x^2+2x+98=0 | | (u^3/10)^2 | | x^2-11x-5=-9x-2 | | -4+6n=-142 | | -3x^2-x^3=0 | | 7y-7=4y+5 | | 71-7x=11x+21 | | 4x+y+5x-y=180 | | 3.5/5.25=16/x | | x^2-9x+15=7 | | x+46x=3x | | 8(4-z)/7=-z | | -11=a-5/6 | | x/12-2=-4 | | -0.5+1.25=3.5n+0.75 | | M/3+4=-2 | | -8x^2+250x+3=0 | | -2=-2u | | -12=-4u | | 8v-12=6(3v+8) | | 13=-1-7x | | 2.4/x=2.4 | | 179-4x=32x+15 | | (x)+(x+2)+(x+4)=2x | | (17b-6)-4(4b+1)=4 | | 4=3-2x | | y-11=13 | | 7.1-9.7x=4.8 | | -3(1-5r)=-36+4r | | 9x^2+35x+30=0 | | 3v^2=22v+16 |

Equations solver categories