3a^2+4a-63=0

Simple and best practice solution for 3a^2+4a-63=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 3a^2+4a-63=0 equation:


Simplifying
3a2 + 4a + -63 = 0

Reorder the terms:
-63 + 4a + 3a2 = 0

Solving
-63 + 4a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-21 + 1.333333333a + a2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 1.333333333a + 21 + a2 = 0 + 21

Reorder the terms:
-21 + 21 + 1.333333333a + a2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 1.333333333a + a2 = 0 + 21
1.333333333a + a2 = 0 + 21

Combine like terms: 0 + 21 = 21
1.333333333a + a2 = 21

The a term is 1.333333333a.  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.
1.333333333a + 0.4444444442 + a2 = 21 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333a + a2 = 21 + 0.4444444442

Combine like terms: 21 + 0.4444444442 = 21.4444444442
0.4444444442 + 1.333333333a + a2 = 21.4444444442

Factor a perfect square on the left side:
(a + 0.6666666665)(a + 0.6666666665) = 21.4444444442

Calculate the square root of the right side: 4.630814663

Break this problem into two subproblems by setting 
(a + 0.6666666665) equal to 4.630814663 and -4.630814663.

Subproblem 1

a + 0.6666666665 = 4.630814663 Simplifying a + 0.6666666665 = 4.630814663 Reorder the terms: 0.6666666665 + a = 4.630814663 Solving 0.6666666665 + a = 4.630814663 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + a = 4.630814663 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + a = 4.630814663 + -0.6666666665 a = 4.630814663 + -0.6666666665 Combine like terms: 4.630814663 + -0.6666666665 = 3.9641479965 a = 3.9641479965 Simplifying a = 3.9641479965

Subproblem 2

a + 0.6666666665 = -4.630814663 Simplifying a + 0.6666666665 = -4.630814663 Reorder the terms: 0.6666666665 + a = -4.630814663 Solving 0.6666666665 + a = -4.630814663 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + a = -4.630814663 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + a = -4.630814663 + -0.6666666665 a = -4.630814663 + -0.6666666665 Combine like terms: -4.630814663 + -0.6666666665 = -5.2974813295 a = -5.2974813295 Simplifying a = -5.2974813295

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.9641479965, -5.2974813295}

See similar equations:

| 100/42 | | 3+5p=-12 | | 4t+16-4= | | 3(x-5)+2x=x+9 | | 2x-8=55-x | | -f+f+3f= | | 2x-8/7(34+65%/7)=5 | | y=18/2 | | (3/4)x24= | | X-.2=138 | | (y^(1/3))/(y^(-3/2)y^(1/2) | | 3d+7d-2d= | | y=7-3(2) | | 9x+7y=-1 | | 47=20m | | 2.9x-6.82=7.1 | | 6v^2-18v-3=0 | | -41+(-49)= | | 8/0.8=0.7x3-0.2^2 | | 2x-6=3x+1-x+7 | | (4)^0(-1)^3/-1 | | 7x*7x-11x+2=0 | | 6+4x=3x | | 7cos^2(x)+7cos^2(x)-7= | | kx^2+x+9k=0 | | 14=3v+7 | | (2a^2)^3/b | | 5x+5=4x+39 | | 5x+5=6x+40 | | 5x+5=3x+40 | | 80=3y+4+1 | | 4x+5=4x+40 |

Equations solver categories