2a^2+3a-7=5

Simple and best practice solution for 2a^2+3a-7=5 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=5 equation:


Simplifying
2a2 + 3a + -7 = 5

Reorder the terms:
-7 + 3a + 2a2 = 5

Solving
-7 + 3a + 2a2 = 5

Solving for variable 'a'.

Reorder the terms:
-7 + -5 + 3a + 2a2 = 5 + -5

Combine like terms: -7 + -5 = -12
-12 + 3a + 2a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-12 + 3a + 2a2 = 0

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

Divide each side by '2'.
-6 + 1.5a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 1.5a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 1.5a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 1.5a + a2 = 0 + 6
1.5a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
1.5a + a2 = 6

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 = 6 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 6 + 0.5625

Combine like terms: 6 + 0.5625 = 6.5625
0.5625 + 1.5a + a2 = 6.5625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(a + 0.75) equal to 2.561737691 and -2.561737691.

Subproblem 1

a + 0.75 = 2.561737691 Simplifying a + 0.75 = 2.561737691 Reorder the terms: 0.75 + a = 2.561737691 Solving 0.75 + a = 2.561737691 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 = 2.561737691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 2.561737691 + -0.75 a = 2.561737691 + -0.75 Combine like terms: 2.561737691 + -0.75 = 1.811737691 a = 1.811737691 Simplifying a = 1.811737691

Subproblem 2

a + 0.75 = -2.561737691 Simplifying a + 0.75 = -2.561737691 Reorder the terms: 0.75 + a = -2.561737691 Solving 0.75 + a = -2.561737691 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 = -2.561737691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -2.561737691 + -0.75 a = -2.561737691 + -0.75 Combine like terms: -2.561737691 + -0.75 = -3.311737691 a = -3.311737691 Simplifying a = -3.311737691

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.811737691, -3.311737691}

See similar equations:

| 2a^2+3a-7= | | 3x^2-8x+18=573 | | 3n+10= | | (2x-5)*(6+x)=2x^2-7x+12 | | 4(3x+5)+7(11x-9)=0 | | 2a^2+3a-7=5k | | -6+x(4)=-5 | | -2y-10=5y+25 | | x+4=7x+32-3x | | 4n-2=5n+18 | | 3x^2-8x+18=523 | | 2a^2+3a-7=30 | | -102=5y | | 2a^2+3a-7=25 | | -101=5y | | 2x+0.25x=3 | | 2a^2+3a-7=10 | | (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 |

Equations solver categories