x^2+1=3x

Simple and best practice solution for x^2+1=3x 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+1=3x equation:


Simplifying
x2 + 1 = 3x

Reorder the terms:
1 + x2 = 3x

Solving
1 + x2 = 3x

Solving for variable 'x'.

Reorder the terms:
1 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
1 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x + x2 = 0 + -1
-3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3x + x2 = -1

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3x + x2 = 1.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -1.5 = 1.118033989 Simplifying x + -1.5 = 1.118033989 Reorder the terms: -1.5 + x = 1.118033989 Solving -1.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.118033989 + 1.5 x = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 x = 2.618033989 Simplifying x = 2.618033989

Subproblem 2

x + -1.5 = -1.118033989 Simplifying x + -1.5 = -1.118033989 Reorder the terms: -1.5 + x = -1.118033989 Solving -1.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.118033989 + 1.5 x = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 x = 0.381966011 Simplifying x = 0.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.618033989, 0.381966011}

See similar equations:

| -6(x+1)-14=24+4 | | 200/12=42/x | | 6(3x-5)-2(x+1)-18x= | | p+.333p=.666 | | 5=6(q-4)-19 | | 21-11y=2 | | x+1/2x+1/2(1/3)x+1/2(1/3)1/2x=42 | | qs=5p-2.5 | | -6n+8(4n+1)=36 | | z^2+47z+18=0 | | qd=15-2p | | 5x^2+5x-20=4 | | (14*50)(50*1/10)(50*1/25) | | g/5-2/5=g/7+4/7 | | 5(-1)-4y=23 | | 2x-13+7x-5=180 | | 2x-13=7x-5 | | 5x-470=365 | | 50(14)-50(1/10x)=50(1/25x) | | 6(0.83m-5)=5(6-5m) | | 2x-13=3x+5 | | 3(7/9) | | l^2+2l+4=192 | | 7/9(3) | | 3(22-x)-2x=26 | | 2x+16+3x-2=180 | | (3x^2+15x-42)/(x-7) | | 7-(-1/15x)(1/20) | | x+2+4x-12=180 | | x^2/6-x=12 | | 2/3*-1 | | (5x^2-2x+9)+(2x^2-4)= |

Equations solver categories