2a^2+3a-7=10

Simple and best practice solution for 2a^2+3a-7=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 2a^2+3a-7=10 equation:


Simplifying
2a2 + 3a + -7 = 10

Reorder the terms:
-7 + 3a + 2a2 = 10

Solving
-7 + 3a + 2a2 = 10

Solving for variable 'a'.

Reorder the terms:
-7 + -10 + 3a + 2a2 = 10 + -10

Combine like terms: -7 + -10 = -17
-17 + 3a + 2a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-17 + 3a + 2a2 = 0

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

Divide each side by '2'.
-8.5 + 1.5a + a2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 1.5a + 8.5 + a2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 1.5a + a2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 1.5a + a2 = 0 + 8.5
1.5a + a2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
1.5a + a2 = 8.5

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = 8.5 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 8.5 + 0.5625

Combine like terms: 8.5 + 0.5625 = 9.0625
0.5625 + 1.5a + a2 = 9.0625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(a + 0.75) equal to 3.010398645 and -3.010398645.

Subproblem 1

a + 0.75 = 3.010398645 Simplifying a + 0.75 = 3.010398645 Reorder the terms: 0.75 + a = 3.010398645 Solving 0.75 + a = 3.010398645 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 3.010398645 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 3.010398645 + -0.75 a = 3.010398645 + -0.75 Combine like terms: 3.010398645 + -0.75 = 2.260398645 a = 2.260398645 Simplifying a = 2.260398645

Subproblem 2

a + 0.75 = -3.010398645 Simplifying a + 0.75 = -3.010398645 Reorder the terms: 0.75 + a = -3.010398645 Solving 0.75 + a = -3.010398645 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -3.010398645 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -3.010398645 + -0.75 a = -3.010398645 + -0.75 Combine like terms: -3.010398645 + -0.75 = -3.760398645 a = -3.760398645 Simplifying a = -3.760398645

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.260398645, -3.760398645}

See similar equations:

| (2x-5)*(6+x)=2x-7x+12 | | 5th-26=18t | | 7t+3=19 | | 10.85/a=3.5 | | -100=5y | | 8x^2=22x-21 | | 2a^2+3a-7=40 | | x+(x-336)=30452 | | 7h-12=51 | | 4x-0.5x-3=0.5 | | t/3-1=16 | | 3G+4g-2g=30 | | 2y^2+9y=(y+2)(y+7) | | 0.8(x+20)+0.6x=65 | | 5v=24 | | 5(f-2)=25 | | .06x+0.09x(x+200)=63 | | 2a^2+3a-7=20 | | 3q+15=21 | | 7+4x=36 | | 78+5y-34=16y-12-3y | | 10(s-5)=-107 | | 26x-3=75 | | 30-5x=6-8x | | 13(t-2)+8t=7(3t+4)-12 | | 9+i=x | | 38+4y-11=14y-13-2y | | 1+9i=x | | 5y+5x=2 | | 8(3s+6)=312 | | 5x+5y=2fory | | 7(2l+7)=133 |

Equations solver categories