21x^2+19x-7=0

Simple and best practice solution for 21x^2+19x-7=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 21x^2+19x-7=0 equation:


Simplifying
21x2 + 19x + -7 = 0

Reorder the terms:
-7 + 19x + 21x2 = 0

Solving
-7 + 19x + 21x2 = 0

Solving for variable 'x'.

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

Divide each side by '21'.
-0.3333333333 + 0.9047619048x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.9047619048x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.9047619048x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.9047619048x + x2 = 0 + 0.3333333333
0.9047619048x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.9047619048x + x2 = 0.3333333333

The x term is 0.9047619048x.  Take half its coefficient (0.4523809524).
Square it (0.2046485261) and add it to both sides.

Add '0.2046485261' to each side of the equation.
0.9047619048x + 0.2046485261 + x2 = 0.3333333333 + 0.2046485261

Reorder the terms:
0.2046485261 + 0.9047619048x + x2 = 0.3333333333 + 0.2046485261

Combine like terms: 0.3333333333 + 0.2046485261 = 0.5379818594
0.2046485261 + 0.9047619048x + x2 = 0.5379818594

Factor a perfect square on the left side:
(x + 0.4523809524)(x + 0.4523809524) = 0.5379818594

Calculate the square root of the right side: 0.733472467

Break this problem into two subproblems by setting 
(x + 0.4523809524) equal to 0.733472467 and -0.733472467.

Subproblem 1

x + 0.4523809524 = 0.733472467 Simplifying x + 0.4523809524 = 0.733472467 Reorder the terms: 0.4523809524 + x = 0.733472467 Solving 0.4523809524 + x = 0.733472467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4523809524' to each side of the equation. 0.4523809524 + -0.4523809524 + x = 0.733472467 + -0.4523809524 Combine like terms: 0.4523809524 + -0.4523809524 = 0.0000000000 0.0000000000 + x = 0.733472467 + -0.4523809524 x = 0.733472467 + -0.4523809524 Combine like terms: 0.733472467 + -0.4523809524 = 0.2810915146 x = 0.2810915146 Simplifying x = 0.2810915146

Subproblem 2

x + 0.4523809524 = -0.733472467 Simplifying x + 0.4523809524 = -0.733472467 Reorder the terms: 0.4523809524 + x = -0.733472467 Solving 0.4523809524 + x = -0.733472467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4523809524' to each side of the equation. 0.4523809524 + -0.4523809524 + x = -0.733472467 + -0.4523809524 Combine like terms: 0.4523809524 + -0.4523809524 = 0.0000000000 0.0000000000 + x = -0.733472467 + -0.4523809524 x = -0.733472467 + -0.4523809524 Combine like terms: -0.733472467 + -0.4523809524 = -1.1858534194 x = -1.1858534194 Simplifying x = -1.1858534194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2810915146, -1.1858534194}

See similar equations:

| In(x)+In(2)=3 | | (5/6)x=24 | | (8-x)*(8x/6) | | -3n+4=10 | | Log(6x^2-6)=log(3x+3) | | x^4+x^3+6*x-36=0 | | 6(2n-5)=6 | | 8x+20=6x+12 | | x-2=2(x+3) | | 7x+27=2x-13 | | 15x-40=12x-70 | | 84a-36b-12c= | | 8x+15=2x+45 | | 84a-91-12c= | | 4y=-4x+4 | | 1/3(9x-3)=-1 | | x-25=36 | | 9/10x8/15 | | 3/4-12i | | 2x+3x+10=60 | | Un=3n-2 | | 5(w-6)=9w-6 | | 1.5x+1.5y=-7.5 | | f(x)=5x^3-7x+13 | | 1800/10000 | | 5x+8=7x+18 | | y+4=2.5(x-1) | | -2h-7-8=-27 | | y+4=2.5(x+1) | | p^2-100p+200=0 | | 3p+9q+15r= | | -1x+6=14 |

Equations solver categories