x^2+3x=24

Simple and best practice solution for x^2+3x=24 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=24 equation:


Simplifying
x2 + 3x = 24

Reorder the terms:
3x + x2 = 24

Solving
3x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 3x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 3x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 3x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 3x + x2 = 0 + 24
3x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
3x + x2 = 24

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 = 24 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 24 + 2.25

Combine like terms: 24 + 2.25 = 26.25
2.25 + 3x + x2 = 26.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

x + 1.5 = 5.123475383 Simplifying x + 1.5 = 5.123475383 Reorder the terms: 1.5 + x = 5.123475383 Solving 1.5 + x = 5.123475383 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 = 5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.123475383 + -1.5 x = 5.123475383 + -1.5 Combine like terms: 5.123475383 + -1.5 = 3.623475383 x = 3.623475383 Simplifying x = 3.623475383

Subproblem 2

x + 1.5 = -5.123475383 Simplifying x + 1.5 = -5.123475383 Reorder the terms: 1.5 + x = -5.123475383 Solving 1.5 + x = -5.123475383 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 = -5.123475383 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.123475383 + -1.5 x = -5.123475383 + -1.5 Combine like terms: -5.123475383 + -1.5 = -6.623475383 x = -6.623475383 Simplifying x = -6.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.623475383, -6.623475383}

See similar equations:

| x+7-2=24 | | 6y-2=4y+6 | | 3=2x-1 | | -0.2x=0.32 | | 8-3z=7z-12 | | (m+3)(-2m^2+5m-1)= | | c^2-5c=0 | | 0.8x=7.2 | | 3x-6y=-15 | | 5w^2+23w+24=0 | | 9x-8y=144 | | 8k-9=5k+21 | | (2r+11)(r-6)= | | 3+4r=23 | | c^2+2c-24= | | (8y^3-7y^2+y)-(9y^2-5y+7)= | | 2x+9y=285 | | 18-1.9z=7.36 | | 10*10= | | 84-3x=33x+16 | | 0.3+0.004t=0.55 | | 5(2+x)-3(3x+2)=5(x-6)+2 | | 6x+5y=305 | | 12-5n+11=2n-8n+3 | | 0.01n-1.5=0.009 | | K^2+6k= | | 7-9x=163-37x | | 7(x+15)-14=28 | | 4(3c-1)-4=10c+6 | | 12x^2-71x-6=0 | | 3.18x-4=8.72 | | x=1-(1-1) |

Equations solver categories