9x=4x^2-1

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


Simplifying
9x = 4x2 + -1

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

Solving
9x = -1 + 4x2

Solving for variable 'x'.

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

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

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

Combine like terms: 4x2 + -4x2 = 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:

| 2x-3=16x+21 | | 4x+20=-x-20 | | Y=(2x+1)(2x+1) | | -5(-2x+7)=60 | | 21c=-205+75+47c | | 15-x+5x=7 | | 16x^2+16y^2-8x-32y=127 | | 13x-6x=-49 | | c+9=3c-5-4c | | i^23=0 | | a+70= | | 3+7s=10s | | (4-5i)-(4+i)=0 | | 12x-24=24 | | (U-1)(u-1)=(u+3)+5 | | 5g-2=-10+9g | | 3n=10.1+9.9 | | 28x+15x+17x= | | 4x-2(2x-8)=2(2x-8)+9x | | -6(2-7x)=114 | | y=-16x^2+23x+9 | | 6*.25+2y=4 | | Tan36=x/10 | | 13x+68+x=180 | | 11x-6+x=180 | | 2x+x-11=88 | | 5k-2=2k-10 | | 4(6+6x)=240 | | 6y+2-(5y)= | | 3p+7=18p-5 | | -7w=-6-6w | | 8x-2+3(3x+6)= |

Equations solver categories