3a^2-5=5a

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


Simplifying
3a2 + -5 = 5a

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

Solving
-5 + 3a2 = 5a

Solving for variable 'a'.

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

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

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

Divide each side by '3'.
-1.666666667 + -1.666666667a + a2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1.666666667a + 1.666666667 + a2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1.666666667a + a2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.666666667a + a2 = 0 + 1.666666667
-1.666666667a + a2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1.666666667a + a2 = 1.666666667

The a term is -1.666666667a.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667a + 0.6944444447 + a2 = 1.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667a + a2 = 1.666666667 + 0.6944444447

Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117
0.6944444447 + -1.666666667a + a2 = 2.3611111117

Factor a perfect square on the left side:
(a + -0.8333333335)(a + -0.8333333335) = 2.3611111117

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(a + -0.8333333335) equal to 1.536590743 and -1.536590743.

Subproblem 1

a + -0.8333333335 = 1.536590743 Simplifying a + -0.8333333335 = 1.536590743 Reorder the terms: -0.8333333335 + a = 1.536590743 Solving -0.8333333335 + a = 1.536590743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + a = 1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + a = 1.536590743 + 0.8333333335 a = 1.536590743 + 0.8333333335 Combine like terms: 1.536590743 + 0.8333333335 = 2.3699240765 a = 2.3699240765 Simplifying a = 2.3699240765

Subproblem 2

a + -0.8333333335 = -1.536590743 Simplifying a + -0.8333333335 = -1.536590743 Reorder the terms: -0.8333333335 + a = -1.536590743 Solving -0.8333333335 + a = -1.536590743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + a = -1.536590743 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + a = -1.536590743 + 0.8333333335 a = -1.536590743 + 0.8333333335 Combine like terms: -1.536590743 + 0.8333333335 = -0.7032574095 a = -0.7032574095 Simplifying a = -0.7032574095

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.3699240765, -0.7032574095}

See similar equations:

| F(x)=-1x+14 | | 5x^2+2x-3=9-9x | | 6x+6=x-6 | | 2(4x+8)+3(2x+1)=5(3+x)-5 | | b+(2b+5)+(2b+5)=95 | | 8+4k=-10 | | 7(2q+1)=4q+11 | | 2(f-3)+7=3f-6 | | 3(6x+9)=9(5+3x) | | 7+3=22 | | 0.70x+0.05(2-x)=0.10(27) | | 4x^2+15x-6=0 | | 6-2(x+4)=-14 | | 8x+8x-36+x=259 | | -5(3-5n)+8n=6n+12 | | 3a-17=1 | | 3x-5=62 | | -0.10(30)+0.45x=0.05(x-12) | | 4g-11=13 | | 6-2(x+4)=14 | | -mx=-y+b | | 4(d-1)=d+5 | | 2p+0(1-p)=0p+2(1-p) | | 6x+x-4=3(x+4) | | 20=19+3(x+8) | | p+0(1-p)=0p+2(1-p) | | -h=-m-p | | 29+10*n=-18*n+91 | | 6x+7=-119 | | 5c-7c+2c+4b-7b= | | x^2+12x-20=2 | | F(x)=-x^2+2x+5 |

Equations solver categories