3x^2+5x-174=0

Simple and best practice solution for 3x^2+5x-174=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 3x^2+5x-174=0 equation:


Simplifying
3x2 + 5x + -174 = 0

Reorder the terms:
-174 + 5x + 3x2 = 0

Solving
-174 + 5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-58 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + 1.666666667x + 58 + x2 = 0 + 58

Reorder the terms:
-58 + 58 + 1.666666667x + x2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + 1.666666667x + x2 = 0 + 58
1.666666667x + x2 = 0 + 58

Combine like terms: 0 + 58 = 58
1.666666667x + x2 = 58

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 58 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 58 + 0.6944444447

Combine like terms: 58 + 0.6944444447 = 58.6944444447
0.6944444447 + 1.666666667x + x2 = 58.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 58.6944444447

Calculate the square root of the right side: 7.661229956

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 7.661229956 and -7.661229956.

Subproblem 1

x + 0.8333333335 = 7.661229956 Simplifying x + 0.8333333335 = 7.661229956 Reorder the terms: 0.8333333335 + x = 7.661229956 Solving 0.8333333335 + x = 7.661229956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 7.661229956 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 7.661229956 + -0.8333333335 x = 7.661229956 + -0.8333333335 Combine like terms: 7.661229956 + -0.8333333335 = 6.8278966225 x = 6.8278966225 Simplifying x = 6.8278966225

Subproblem 2

x + 0.8333333335 = -7.661229956 Simplifying x + 0.8333333335 = -7.661229956 Reorder the terms: 0.8333333335 + x = -7.661229956 Solving 0.8333333335 + x = -7.661229956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -7.661229956 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -7.661229956 + -0.8333333335 x = -7.661229956 + -0.8333333335 Combine like terms: -7.661229956 + -0.8333333335 = -8.4945632895 x = -8.4945632895 Simplifying x = -8.4945632895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.8278966225, -8.4945632895}

See similar equations:

| x+20=24 | | 3x^2+5x-174=o | | -41=-x | | (x-1)(x+6)=10x | | 2x+2x*2+6=34 | | y+20=25 | | 6b^2-24b+24= | | -8.3x=74.7 | | 5x-7=-3x+23 | | 2x+2x*2+6=24 | | 4x^2+6x=10 | | 2x^2+13x+21=0 | | s(s+1)=72 | | z-17=-3 | | -8.2x=41.0 | | 2(3.5)=2.5n-2 | | 8c+2c=30 | | 3x+6=3(x-4)+18 | | K+20=-10 | | 2x-20=40 | | 4b+7b-1.6=1.7 | | 4(3-x)+1=2x-2-3x | | 5x-4y=7 | | 12=11(-4)-14(-4) | | 2x-7=-10 | | -8.7x=78.3 | | 6z-1=13 | | 12=11x-14x | | x+5+3x+x=180 | | 2x^2-4x-198=0 | | 2x^2-4x-198=o | | -3x-1=-64 |

Equations solver categories