4x^2+29x-10=0

Simple and best practice solution for 4x^2+29x-10=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 4x^2+29x-10=0 equation: 


Simplifying
4x2 + 29x + -10 = 0

Reorder the terms:
-10 + 29x + 4x2 = 0

Solving
-10 + 29x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-2.5 + 7.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 7.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 7.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 7.25x + x2 = 0 + 2.5
7.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
7.25x + x2 = 2.5

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = 2.5 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = 2.5 + 13.140625

Combine like terms: 2.5 + 13.140625 = 15.640625
13.140625 + 7.25x + x2 = 15.640625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 15.640625

Calculate the square root of the right side: 3.954823005

Break this problem into two subproblems by setting 
(x + 3.625) equal to 3.954823005 and -3.954823005.


Subproblem 1
x + 3.625 = 3.954823005

Simplifying
x + 3.625 = 3.954823005

Reorder the terms:
3.625 + x = 3.954823005

Solving
3.625 + x = 3.954823005

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = 3.954823005 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = 3.954823005 + -3.625
x = 3.954823005 + -3.625

Combine like terms: 3.954823005 + -3.625 = 0.329823005
x = 0.329823005

Simplifying
x = 0.329823005


Subproblem 2
x + 3.625 = -3.954823005

Simplifying
x + 3.625 = -3.954823005

Reorder the terms:
3.625 + x = -3.954823005

Solving
3.625 + x = -3.954823005

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = -3.954823005 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = -3.954823005 + -3.625
x = -3.954823005 + -3.625

Combine like terms: -3.954823005 + -3.625 = -7.579823005
x = -7.579823005

Simplifying
x = -7.579823005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.329823005, -7.579823005}

See similar equations:

| 30-4x/2 | | 4/81-y^4 | | 4x-1+18x=16(x-3)(x-4) | | -a+(1+6a)=88 | | n-11=28 | | 8(3q+1)-4(1+4q)= | | -m-4-6=10 | | 12/3/5 | | n+5-2N=1 | | 6(2y+1)-3(2+3y)= | | 5(p+5)-4(5p+1)= | | 17-x=12-2 | | 9-2y/25-y^2 | | n-7=19 | | 3+2n+2=9 | | -3(4x-1)+4(2x+3)=-4(x-3) | | 3(m+3)-4(3m+2)= | | 7(a+4)-2(2a+1)= | | 3-(-2)= | | 3x*6=5 | | 1-7x+6=21 | | 10=sp | | -(2z+7)=13 | | 6(t+7)=9+t | | 96/(x+7) | | -8(w-1)=5w-44 | | 3n(m+2n)= | | 3.6=45/I | | 2a+b-4a+5b= | | (x-2)(x+2)+3x=(4+x)(x-4) | | -8y+22=9(y-7) | | 9/(2x+2) |

Equations solver categories