3x^2+21x+7=0

Simple and best practice solution for 3x^2+21x+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 3x^2+21x+7=0 equation:


Simplifying
3x2 + 21x + 7 = 0

Reorder the terms:
7 + 21x + 3x2 = 0

Solving
7 + 21x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2.333333333 + 7x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 7x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 7x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 7x + x2 = 0 + -2.333333333
7x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
7x + x2 = -2.333333333

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 = -2.333333333 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2.333333333 + 12.25

Combine like terms: -2.333333333 + 12.25 = 9.916666667
12.25 + 7x + x2 = 9.916666667

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 9.916666667

Calculate the square root of the right side: 3.149073938

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.149073938 and -3.149073938.

Subproblem 1

x + 3.5 = 3.149073938 Simplifying x + 3.5 = 3.149073938 Reorder the terms: 3.5 + x = 3.149073938 Solving 3.5 + x = 3.149073938 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 = 3.149073938 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.149073938 + -3.5 x = 3.149073938 + -3.5 Combine like terms: 3.149073938 + -3.5 = -0.350926062 x = -0.350926062 Simplifying x = -0.350926062

Subproblem 2

x + 3.5 = -3.149073938 Simplifying x + 3.5 = -3.149073938 Reorder the terms: 3.5 + x = -3.149073938 Solving 3.5 + x = -3.149073938 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 = -3.149073938 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.149073938 + -3.5 x = -3.149073938 + -3.5 Combine like terms: -3.149073938 + -3.5 = -6.649073938 x = -6.649073938 Simplifying x = -6.649073938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.350926062, -6.649073938}

See similar equations:

| -2+2(7+8n)=124 | | 6+2s=3+20s | | 8(m+6)=-88 | | 3-6(4+7x)=-231 | | 3(2y-7)-2y=3 | | -3(6+3a)+8=-82 | | 90-4x=41x+15 | | 2(-3)=y-10 | | 7x-7=-3 | | 5(x-3)-4(3x-7)= | | 10+.10A=0+.35A | | 2x=(x+7)-10 | | 0=4x^2-17x-15 | | -2x+8x^2+6y+2x+18y= | | 5a-5=7+29 | | 0.1(-7.09+6x)=0.7x | | 4x^2-x+3y+4x^2-x+3y= | | x+9y+x+9y= | | 9/8=(-1/3)u | | 0=x^2-225 | | 3r-20=25 | | 3w=5/9 | | 8.4y-7.4y+2.6=-4.9 | | 36000+1200y=28000+2600y | | 4/3=w-5/3 | | 13=v+4 | | -5=-5(x+5)-2x | | (-3x^2y^4)(7x^5y^3)=0 | | -0.02f+0.8+21=6 | | 17z+4=9z-40 | | 0=x^2-8x+16 | | 7r+3.5-5r=9.5 |

Equations solver categories