x(2x-3)=23

Simple and best practice solution for x(2x-3)=23 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(2x-3)=23 equation:


Simplifying
x(2x + -3) = 23

Reorder the terms:
x(-3 + 2x) = 23
(-3 * x + 2x * x) = 23
(-3x + 2x2) = 23

Solving
-3x + 2x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + -3x + 2x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -3x + 2x2 = 0

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

Divide each side by '2'.
-11.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -1.5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -1.5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -1.5x + x2 = 0 + 11.5
-1.5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
-1.5x + x2 = 11.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 11.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 11.5 + 0.5625

Combine like terms: 11.5 + 0.5625 = 12.0625
0.5625 + -1.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + -0.75 = 3.473110997 Simplifying x + -0.75 = 3.473110997 Reorder the terms: -0.75 + x = 3.473110997 Solving -0.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.473110997 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.473110997 + 0.75 x = 3.473110997 + 0.75 Combine like terms: 3.473110997 + 0.75 = 4.223110997 x = 4.223110997 Simplifying x = 4.223110997

Subproblem 2

x + -0.75 = -3.473110997 Simplifying x + -0.75 = -3.473110997 Reorder the terms: -0.75 + x = -3.473110997 Solving -0.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.473110997 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.473110997 + 0.75 x = -3.473110997 + 0.75 Combine like terms: -3.473110997 + 0.75 = -2.723110997 x = -2.723110997 Simplifying x = -2.723110997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.223110997, -2.723110997}

See similar equations:

| (7x6/3)x3-(2+3-4) | | -4(-6y-17)-11y=9(18y-9) | | (5x-1)7=-2 | | 5x=56+6 | | 20x=16x+15 | | y=-6/5(-4)+31/5 | | 6x+x/3+18 | | z/8=-26 | | (X-4)(2x+5)=o | | -1/8(n+6)=-1/9(n+2) | | (4z-10)+1z=90 | | (6x+10)/11=-4 | | 7/(4x-1)=2/(x+5) | | -6/5(-4)+31/5 | | 15=6a-24-9a | | 7-3x=1/4(8x-12) | | 2T=T-(84*.5) | | 6x^7/5-66=0 | | 9xy^2*9x^5y^2= | | 6m+9(2-m)=2(7-4m)-11 | | 15(x^2+2x)= | | 1+999= | | 3+6(7n+3)=-147 | | 4(9-3)/(8-2) | | 18(-y-2)-4(-9+3y)+76=-14 | | 9x+4+3x=7x+x+14 | | -3/4(-x-8)=x+10 | | y=8+2z | | -4/5(z+3)=-2/3(z-4/5) | | a=(w)(3w) | | 3y+2-4y=9 | | 2/3/1/8 |

Equations solver categories