2a^2-18a+20.25=0

Simple and best practice solution for 2a^2-18a+20.25=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 2a^2-18a+20.25=0 equation:


Simplifying
2a2 + -18a + 20.25 = 0

Reorder the terms:
20.25 + -18a + 2a2 = 0

Solving
20.25 + -18a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
10.125 + -9a + a2 = 0

Move the constant term to the right:

Add '-10.125' to each side of the equation.
10.125 + -9a + -10.125 + a2 = 0 + -10.125

Reorder the terms:
10.125 + -10.125 + -9a + a2 = 0 + -10.125

Combine like terms: 10.125 + -10.125 = 0.000
0.000 + -9a + a2 = 0 + -10.125
-9a + a2 = 0 + -10.125

Combine like terms: 0 + -10.125 = -10.125
-9a + a2 = -10.125

The a term is -9a.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9a + 20.25 + a2 = -10.125 + 20.25

Reorder the terms:
20.25 + -9a + a2 = -10.125 + 20.25

Combine like terms: -10.125 + 20.25 = 10.125
20.25 + -9a + a2 = 10.125

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 10.125

Calculate the square root of the right side: 3.181980515

Break this problem into two subproblems by setting 
(a + -4.5) equal to 3.181980515 and -3.181980515.

Subproblem 1

a + -4.5 = 3.181980515 Simplifying a + -4.5 = 3.181980515 Reorder the terms: -4.5 + a = 3.181980515 Solving -4.5 + a = 3.181980515 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 3.181980515 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 3.181980515 + 4.5 a = 3.181980515 + 4.5 Combine like terms: 3.181980515 + 4.5 = 7.681980515 a = 7.681980515 Simplifying a = 7.681980515

Subproblem 2

a + -4.5 = -3.181980515 Simplifying a + -4.5 = -3.181980515 Reorder the terms: -4.5 + a = -3.181980515 Solving -4.5 + a = -3.181980515 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -3.181980515 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -3.181980515 + 4.5 a = -3.181980515 + 4.5 Combine like terms: -3.181980515 + 4.5 = 1.318019485 a = 1.318019485 Simplifying a = 1.318019485

Solution

The solution to the problem is based on the solutions from the subproblems. a = {7.681980515, 1.318019485}

See similar equations:

| x-3(17)=81 | | F(X)=(32-x)(40-x) | | x+2=5x+22 | | 2kx^2+kx-x=0 | | 3X+1=48 | | 4x+y=-x+9 | | 2x+3=61 | | 6(-2-9k)= | | 3x-1.66=-7(3.5x-3)-3 | | 2(6+5x)=102 | | 4x=81+x | | -29x+6.1=-5(5.8x+2.2)-0.3 | | a+0.05a= | | -45x-1=9(-5x+1)-4 | | -15=5x+10 | | (x+3)(x-4)=-12 | | (2x+3)(6-3x)=0 | | (-8x+8)2=4 | | (50-2x)*(25x+400)=204000 | | 34x+23.4=4(8.5x+4.1)+7 | | 7x+4y=4 | | -10x+17=-2(5x-5)+7 | | lnx+2+lnx+2=6 | | 2x-7=-14 | | log[5]5=x | | x*log[5](x)=18 | | (25k^2)=30 | | F(x+3)=x^2+kx-21 | | x^3+4x^2-19+14=0 | | x*(x-7)=228 | | =sin(9x) | | y=sin(9*x) |

Equations solver categories