4x^2=9x+1

Simple and best practice solution for 4x^2=9x+1 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 4x^2=9x+1 equation:


Simplifying
4x2 = 9x + 1

Reorder the terms:
4x2 = 1 + 9x

Solving
4x2 = 1 + 9x

Solving for variable 'x'.

Reorder the terms:
-1 + -9x + 4x2 = 1 + 9x + -1 + -9x

Reorder the terms:
-1 + -9x + 4x2 = 1 + -1 + 9x + -9x

Combine like terms: 1 + -1 = 0
-1 + -9x + 4x2 = 0 + 9x + -9x
-1 + -9x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-1 + -9x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + -2.25x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.25x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.25x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.25x + x2 = 0 + 0.25
-2.25x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.25x + x2 = 0.25

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 0.25 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 0.25 + 1.265625

Combine like terms: 0.25 + 1.265625 = 1.515625
1.265625 + -2.25x + x2 = 1.515625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.231107225 and -1.231107225.

Subproblem 1

x + -1.125 = 1.231107225 Simplifying x + -1.125 = 1.231107225 Reorder the terms: -1.125 + x = 1.231107225 Solving -1.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.231107225 + 1.125 x = 1.231107225 + 1.125 Combine like terms: 1.231107225 + 1.125 = 2.356107225 x = 2.356107225 Simplifying x = 2.356107225

Subproblem 2

x + -1.125 = -1.231107225 Simplifying x + -1.125 = -1.231107225 Reorder the terms: -1.125 + x = -1.231107225 Solving -1.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.231107225 + 1.125 x = -1.231107225 + 1.125 Combine like terms: -1.231107225 + 1.125 = -0.106107225 x = -0.106107225 Simplifying x = -0.106107225

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.356107225, -0.106107225}

See similar equations:

| 5X+4=2X+41 | | x*y=63 | | .33(m+6)+.2m=7 | | 5(2+x)=8(20-x) | | 5(3ax+y)=8ax-3yforx | | 1080b^3+5= | | 9(9g+6)/2 | | 9d+5=6d+8 | | 2+y/2=5y/8-3 | | 7c-8=14 | | 3/8(y+7)+5/6(2y-3) | | 4(b-2)=6(a+1) | | 3x^2-16x=-13 | | -8+4+36=6n-4 | | 5-7x=53-35x | | 15,8x+7,8-8,4x=30 | | 7-3b=-11 | | -17x-3x=13-9x | | 2x+38=10x-75 | | 6x=2x+3x+42 | | 4,2x-2,6=3,2+1,3x | | 3.50*4= | | 5x+56=9x+14 | | 4(x+25)=3(7+x) | | 1043+72x=4x+2131 | | 113-21x=x+x-186 | | x=2x+3x+42 | | 1+3x/2+2-x/3=5/6 | | 9(4g+5)= | | x=1,2x+1,3x+7 | | 245-17x=9+63 | | 4n-(7)=10 |

Equations solver categories