24x^2-75x-29=0

Simple and best practice solution for 24x^2-75x-29=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 24x^2-75x-29=0 equation:


Simplifying
24x2 + -75x + -29 = 0

Reorder the terms:
-29 + -75x + 24x2 = 0

Solving
-29 + -75x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
-1.208333333 + -3.125x + x2 = 0

Move the constant term to the right:

Add '1.208333333' to each side of the equation.
-1.208333333 + -3.125x + 1.208333333 + x2 = 0 + 1.208333333

Reorder the terms:
-1.208333333 + 1.208333333 + -3.125x + x2 = 0 + 1.208333333

Combine like terms: -1.208333333 + 1.208333333 = 0.000000000
0.000000000 + -3.125x + x2 = 0 + 1.208333333
-3.125x + x2 = 0 + 1.208333333

Combine like terms: 0 + 1.208333333 = 1.208333333
-3.125x + x2 = 1.208333333

The x term is -3.125x.  Take half its coefficient (-1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
-3.125x + 2.44140625 + x2 = 1.208333333 + 2.44140625

Reorder the terms:
2.44140625 + -3.125x + x2 = 1.208333333 + 2.44140625

Combine like terms: 1.208333333 + 2.44140625 = 3.649739583
2.44140625 + -3.125x + x2 = 3.649739583

Factor a perfect square on the left side:
(x + -1.5625)(x + -1.5625) = 3.649739583

Calculate the square root of the right side: 1.910429162

Break this problem into two subproblems by setting 
(x + -1.5625) equal to 1.910429162 and -1.910429162.

Subproblem 1

x + -1.5625 = 1.910429162 Simplifying x + -1.5625 = 1.910429162 Reorder the terms: -1.5625 + x = 1.910429162 Solving -1.5625 + x = 1.910429162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.910429162 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.910429162 + 1.5625 x = 1.910429162 + 1.5625 Combine like terms: 1.910429162 + 1.5625 = 3.472929162 x = 3.472929162 Simplifying x = 3.472929162

Subproblem 2

x + -1.5625 = -1.910429162 Simplifying x + -1.5625 = -1.910429162 Reorder the terms: -1.5625 + x = -1.910429162 Solving -1.5625 + x = -1.910429162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.910429162 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.910429162 + 1.5625 x = -1.910429162 + 1.5625 Combine like terms: -1.910429162 + 1.5625 = -0.347929162 x = -0.347929162 Simplifying x = -0.347929162

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.472929162, -0.347929162}

See similar equations:

| 70=x+60 | | 3x-3=4x-9 | | 3(x-3)=4x-9 | | 3k^2+72-33k=0 | | 4t-3=15 | | 9(y-1)=4y+16 | | 4x+(3x-8)=5x-7 | | (6y+8)(4y-10)=0 | | 2x-4=4x-6 | | 12x-27=105 | | 220=2w+2l | | 5-x+(4x-1)=2x+6 | | 9(y-1)=4y+26 | | 15-2x=3+2 | | 15=x+20 | | 6x+6x+4+9=7x+5+4x | | 25000=2000t | | 14x=180 | | (28b-8)-9(3b+4)=-6 | | 14-5x=-61 | | -5=4x-13 | | x^4+3x^2-8x+10=0 | | 6x+15=105 | | 8x+16=136 | | 3x+8-2x=18 | | A=15(2)*39+21 | | 5(7g+6)=120 | | 16x+4=8x+76 | | 3x+4-(5x-7)= | | 8(x-7)=-40 | | 6x-3+x+2= | | 13d+5=6d+68 |

Equations solver categories