2a^2-152a=180

Simple and best practice solution for 2a^2-152a=180 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^2-152a=180 equation:


Simplifying
2a2 + -152a = 180

Reorder the terms:
-152a + 2a2 = 180

Solving
-152a + 2a2 = 180

Solving for variable 'a'.

Reorder the terms:
-180 + -152a + 2a2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -152a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -76a + a2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-90 + -76a + a2)' equal to zero and attempt to solve: Simplifying -90 + -76a + a2 = 0 Solving -90 + -76a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -76a + 90 + a2 = 0 + 90 Reorder the terms: -90 + 90 + -76a + a2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -76a + a2 = 0 + 90 -76a + a2 = 0 + 90 Combine like terms: 0 + 90 = 90 -76a + a2 = 90 The a term is -76a. Take half its coefficient (-38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. -76a + 1444 + a2 = 90 + 1444 Reorder the terms: 1444 + -76a + a2 = 90 + 1444 Combine like terms: 90 + 1444 = 1534 1444 + -76a + a2 = 1534 Factor a perfect square on the left side: (a + -38)(a + -38) = 1534 Calculate the square root of the right side: 39.166312055 Break this problem into two subproblems by setting (a + -38) equal to 39.166312055 and -39.166312055.

Subproblem 1

a + -38 = 39.166312055 Simplifying a + -38 = 39.166312055 Reorder the terms: -38 + a = 39.166312055 Solving -38 + a = 39.166312055 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + a = 39.166312055 + 38 Combine like terms: -38 + 38 = 0 0 + a = 39.166312055 + 38 a = 39.166312055 + 38 Combine like terms: 39.166312055 + 38 = 77.166312055 a = 77.166312055 Simplifying a = 77.166312055

Subproblem 2

a + -38 = -39.166312055 Simplifying a + -38 = -39.166312055 Reorder the terms: -38 + a = -39.166312055 Solving -38 + a = -39.166312055 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + a = -39.166312055 + 38 Combine like terms: -38 + 38 = 0 0 + a = -39.166312055 + 38 a = -39.166312055 + 38 Combine like terms: -39.166312055 + 38 = -1.166312055 a = -1.166312055 Simplifying a = -1.166312055

Solution

The solution to the problem is based on the solutions from the subproblems. a = {77.166312055, -1.166312055}

Solution

a = {77.166312055, -1.166312055}

See similar equations:

| 2a^2-15a=180 | | -3(0)-y=0 | | 6(0)-4y=-24 | | x=2(5) | | 6(6)-4y=-24 | | 9x-y=83 | | 1/2(360-x)-x=104 | | 3x-2(0)=-18 | | 6x+1=-x+15 | | (2/(3x))+(1/2)=(4/x)+(4/3) | | 3(0)-2y=-18 | | s^2-3(s+3)=4 | | 0.23x+0.18=0.08x-0.27 | | 2y-4=8y+2 | | 8d+3=6-2d | | y+36=43 | | f(x)=-2x^2-12x-14 | | 10x+4y=35 | | 4.2x-5=3.2x-5 | | (1/6-11/12)(-7/8+1/3+1/6) | | -5(w+3)+3(w+1)=14 | | 3x=2-(-1) | | x^2+y^9=0 | | 4(x-7)=524 | | X-3x=-18x | | 3(1)=2-y | | 10y-16y+5=0 | | 5x+1+5x+2=3750 | | 4x+2(-1)=-18 | | 4(-4)+2y=-18 | | 3x+5(-1)=-17 | | x^3-9X+5=0 |

Equations solver categories