3x^2+4x+4=10

Simple and best practice solution for 3x^2+4x+4=10 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+4x+4=10 equation:


Simplifying
3x2 + 4x + 4 = 10

Reorder the terms:
4 + 4x + 3x2 = 10

Solving
4 + 4x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
4 + -10 + 4x + 3x2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + 4x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + 4x + 3x2 = 0

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

Divide each side by '3'.
-2 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.333333333x + x2 = 0 + 2
1.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.333333333x + x2 = 2

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 2 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 2 + 0.4444444442

Combine like terms: 2 + 0.4444444442 = 2.4444444442
0.4444444442 + 1.333333333x + x2 = 2.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 2.4444444442

Calculate the square root of the right side: 1.56347192

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.56347192 and -1.56347192.

Subproblem 1

x + 0.6666666665 = 1.56347192 Simplifying x + 0.6666666665 = 1.56347192 Reorder the terms: 0.6666666665 + x = 1.56347192 Solving 0.6666666665 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.56347192 + -0.6666666665 x = 1.56347192 + -0.6666666665 Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535 x = 0.8968052535 Simplifying x = 0.8968052535

Subproblem 2

x + 0.6666666665 = -1.56347192 Simplifying x + 0.6666666665 = -1.56347192 Reorder the terms: 0.6666666665 + x = -1.56347192 Solving 0.6666666665 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.56347192 + -0.6666666665 x = -1.56347192 + -0.6666666665 Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865 x = -2.2301385865 Simplifying x = -2.2301385865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8968052535, -2.2301385865}

See similar equations:

| 5x-12+6x+27=180 | | -(1/2)w-(3/5)=(1/5)w | | -.5w-(3/5)=(1/5)w | | 13p=52 | | 6r-7=13-7r | | 3xyz+4yz+4z=-7 | | -3(10+-10p)+10p= | | 5x+3+8x+4=10 | | 4x^2-24=10 | | 5.6+9.4= | | S-7=39 | | y=-2x-15 | | 14x-2=12x+7 | | 3xyz+4yz+4z+k=1000000 | | 10k+3=9(k-3) | | x+(x-4)=8 | | 5x+3=2(x+3)-6+3x | | 7x+6-3x=-5x-15+x | | 10+7(8c+2)= | | x+1.23x=3000 | | 5x+3(x-1)=7 | | 90+x^2+3x=180 | | 9=4v-v | | 3xyz+4yz+4z+8=1 | | 5(m+5)+3=25 | | N+14=50 | | t(x)=3x^2-30x-12 | | 7x+1+7x+1=3x+24 | | 3me+9=15z | | y=5(3y+1)+2 | | 3-5w+6= | | 6(-7-5x)=42 |

Equations solver categories