4X^2-X-9=0

Simple and best practice solution for 4X^2-X-9=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 4X^2-X-9=0 equation:


Simplifying
4X2 + -1X + -9 = 0

Reorder the terms:
-9 + -1X + 4X2 = 0

Solving
-9 + -1X + 4X2 = 0

Solving for variable 'X'.

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

Divide each side by '4'.
-2.25 + -0.25X + X2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -0.25X + 2.25 + X2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -0.25X + X2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -0.25X + X2 = 0 + 2.25
-0.25X + X2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-0.25X + X2 = 2.25

The X term is -0.25X.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25X + 0.015625 + X2 = 2.25 + 0.015625

Reorder the terms:
0.015625 + -0.25X + X2 = 2.25 + 0.015625

Combine like terms: 2.25 + 0.015625 = 2.265625
0.015625 + -0.25X + X2 = 2.265625

Factor a perfect square on the left side:
(X + -0.125)(X + -0.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(X + -0.125) equal to 1.505199322 and -1.505199322.

Subproblem 1

X + -0.125 = 1.505199322 Simplifying X + -0.125 = 1.505199322 Reorder the terms: -0.125 + X = 1.505199322 Solving -0.125 + X = 1.505199322 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = 1.505199322 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = 1.505199322 + 0.125 X = 1.505199322 + 0.125 Combine like terms: 1.505199322 + 0.125 = 1.630199322 X = 1.630199322 Simplifying X = 1.630199322

Subproblem 2

X + -0.125 = -1.505199322 Simplifying X + -0.125 = -1.505199322 Reorder the terms: -0.125 + X = -1.505199322 Solving -0.125 + X = -1.505199322 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + X = -1.505199322 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + X = -1.505199322 + 0.125 X = -1.505199322 + 0.125 Combine like terms: -1.505199322 + 0.125 = -1.380199322 X = -1.380199322 Simplifying X = -1.380199322

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.630199322, -1.380199322}

See similar equations:

| 18x-7=73-2x | | 7z+3-(6z-3)=15z+6 | | 2+3(2-x)=0.5x-2(x+2) | | 108-4x=32x+24 | | 16-2x+1=11 | | 3(7y+9)-8(5y-2)=62 | | 3x+x+2=x+20 | | 2x^2+7x-184=0 | | 25x+x^2=0 | | (7z+3)-(6z-3)=15z+6 | | 2x^2-13x-70=0 | | (7/15)x-(1/5)=4 | | 16-(2x+1)=11 | | 0.16*0.01(x+1)=-0.03(3-x) | | 12x^2-60x+7=0 | | 2(x-3)=3(x+7) | | 3x+(x+2)=x+20 | | -2x+5=-5x | | -17+2x=15 | | -5(3-x)=2x+7 | | 5(x-2)=2x | | 2(x+1)=3 | | 6-5x=2x+5 | | 3x^2+x=30 | | 3+0*x-1=2 | | 3*x-1=2 | | 0*x+4=-3 | | 133+7x-20=4x+33 | | 18x^2=9 | | -18-6=14-10x | | -2(3x-5)+8x-2= | | -12x+7=5x-2x^2 |

Equations solver categories