x^2=5x-1

Simple and best practice solution for x^2=5x-1 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=5x-1 equation:


Simplifying
x2 = 5x + -1

Reorder the terms:
x2 = -1 + 5x

Solving
x2 = -1 + 5x

Solving for variable 'x'.

Reorder the terms:
1 + -5x + x2 = -1 + 5x + 1 + -5x

Reorder the terms:
1 + -5x + x2 = -1 + 1 + 5x + -5x

Combine like terms: -1 + 1 = 0
1 + -5x + x2 = 0 + 5x + -5x
1 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
1 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x + x2 = 0 + -1
-5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5x + x2 = -1

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 = -1 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + -5x + x2 = 5.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + -2.5 = 2.291287847 Simplifying x + -2.5 = 2.291287847 Reorder the terms: -2.5 + x = 2.291287847 Solving -2.5 + x = 2.291287847 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 = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.291287847 + 2.5 x = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 x = 4.791287847 Simplifying x = 4.791287847

Subproblem 2

x + -2.5 = -2.291287847 Simplifying x + -2.5 = -2.291287847 Reorder the terms: -2.5 + x = -2.291287847 Solving -2.5 + x = -2.291287847 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 = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.291287847 + 2.5 x = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 x = 0.208712153 Simplifying x = 0.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.791287847, 0.208712153}

See similar equations:

| 6x-9=-17 | | 4x^2=25-15x | | Y=-2(x+1)(x-5) | | (3x-2)/10-(4x+1)/4=-4 | | iz^2-4iz+4i=8 | | f=.5kq | | -.01+60=0 | | -5s=-30 | | x^2+8x=9x+42 | | .01+60x=100 | | -60-1x=100 | | (5x+46)^1/2=3x+12 | | z^2-16z+64=-256 | | 5b-3-9b-7= | | (9X+45)^1/2=2X+8 | | (5X+24)^1/2=3X+16 | | (5X-24)^1/2=3X+16 | | 3(k+4)-8k+4+2= | | -(11x-5)-(2x-6)+6=-6(x-1)-(12x+7)+3 | | (-4/5)/(3/2) | | c-3c= | | -4/5/3/2 | | -5(4y-6)+4(2y+6)= | | 6(3y+7)+(-28y)= | | y^2=-6x+5 | | 2x^2(x+3)=-4x^2(x-1) | | 17+5(6c-3)= | | 12(3x+3)-6(2x-5)=4x-54 | | 40-[4+8y-3(y+2)]=-3(5y-7)-[8(y-1)-13y+17] | | 40-[4+8y-3(y+2)]=-3(5y-7)-[8(y-1)-13y+13] | | 26=5(x+6)-7x | | 11=3(x-3)-(x-6) |

Equations solver categories