4x^2-20x+13=0

Simple and best practice solution for 4x^2-20x+13=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^2-20x+13=0 equation:


Simplifying
4x2 + -20x + 13 = 0

Reorder the terms:
13 + -20x + 4x2 = 0

Solving
13 + -20x + 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'.
3.25 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -5x + -3.25 + x2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + -5x + x2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -5x + x2 = 0 + -3.25
-5x + x2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
-5x + x2 = -3.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.25 + 6.25

Combine like terms: -3.25 + 6.25 = 3
6.25 + -5x + x2 = 3

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + -2.5 = 1.732050808 Simplifying x + -2.5 = 1.732050808 Reorder the terms: -2.5 + x = 1.732050808 Solving -2.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.732050808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.732050808 + 2.5 x = 1.732050808 + 2.5 Combine like terms: 1.732050808 + 2.5 = 4.232050808 x = 4.232050808 Simplifying x = 4.232050808

Subproblem 2

x + -2.5 = -1.732050808 Simplifying x + -2.5 = -1.732050808 Reorder the terms: -2.5 + x = -1.732050808 Solving -2.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.732050808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.732050808 + 2.5 x = -1.732050808 + 2.5 Combine like terms: -1.732050808 + 2.5 = 0.767949192 x = 0.767949192 Simplifying x = 0.767949192

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.232050808, 0.767949192}

See similar equations:

| -(5y+4)-(-4y-5)=-7 | | -18x+2=-7x+2 | | r^2+9r-110=0 | | 16x^2-64x+62=0 | | 4x^2+24x=-20 | | -14=-7+y | | 4a^2+4a-15= | | 16(2x-8)=4(8x+2) | | 7-9x-5-3x=5 | | 6(x+2)=3x+48 | | 9+12m-3=4m+66-2m | | x(x+6)-88=0 | | 2x-4=-2x+8 | | -3x+6=42 | | 30-8y=4 | | 3s+5s=32 | | 22-4x=12 | | x^2+6-88=0 | | n^2-30=0 | | 4(4+4x)-6= | | 3c+5c+20=68 | | 8=s+8 | | 5(4x+3)-4x= | | -11.5x=80.5 | | 2t=-22 | | 6z=-30 | | 5+10x=0 | | 2(x+1)=-4(x+2)+22 | | -7(2b+2)+(15b-6)=0 | | -(7y+3)-(-6y-8)=5 | | 5.6q-5.4-5.4q=-0.8q-4.9 | | -1*-2= |

Equations solver categories