x^2-3x-23=0

Simple and best practice solution for x^2-3x-23=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 x^2-3x-23=0 equation:


Simplifying
x2 + -3x + -23 = 0

Reorder the terms:
-23 + -3x + x2 = 0

Solving
-23 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -3x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + -3x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -3x + x2 = 0 + 23
-3x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
-3x + x2 = 23

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 23 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 23 + 2.25

Combine like terms: 23 + 2.25 = 25.25
2.25 + -3x + x2 = 25.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(x + -1.5) equal to 5.024937811 and -5.024937811.

Subproblem 1

x + -1.5 = 5.024937811 Simplifying x + -1.5 = 5.024937811 Reorder the terms: -1.5 + x = 5.024937811 Solving -1.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.024937811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.024937811 + 1.5 x = 5.024937811 + 1.5 Combine like terms: 5.024937811 + 1.5 = 6.524937811 x = 6.524937811 Simplifying x = 6.524937811

Subproblem 2

x + -1.5 = -5.024937811 Simplifying x + -1.5 = -5.024937811 Reorder the terms: -1.5 + x = -5.024937811 Solving -1.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.024937811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.024937811 + 1.5 x = -5.024937811 + 1.5 Combine like terms: -5.024937811 + 1.5 = -3.524937811 x = -3.524937811 Simplifying x = -3.524937811

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.524937811, -3.524937811}

See similar equations:

| 2a^2-15a-18=0 | | 2t+1+2t-3t=6+2 | | c^2-8c-36= | | -29-7k=2(1k+8) | | x+3+2x+4+3x-7= | | 3x-x=26 | | 2a^2-15-18=0 | | 5x-23+x=7 | | 11=x/8 | | 4.8/0.6 | | 6.4s-9=5.4s-9 | | 9x-5+3x=31 | | -4(5v-1)+8v=8+3(2v-4) | | 3/x+4-7=18/x+4 | | 10y^5+28y^4-6y^3=0 | | 5k-(-9k)=-70 | | 3x+(3x+5)+(7x+6)=180 | | 4x+15-x=12 | | -8y+2=-9y+7 | | 2x^2+11xy+14y^2=0 | | 3a=0.39 | | 6+6x=8y | | 7+16y= | | 2x+12=3x+9 | | x/5=(x/11)+12 | | 2/3x+5/4=13/6x+5/3 | | 9a-(-72)= | | -5(w-2)=(-2)w-5 | | 2x^2-13xy-24y^2=0 | | -15-15= | | (x+6/9)=(x/6)+(1/2) | | -32-5n=7(n-8) |

Equations solver categories