x^2=3x+5

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


Simplifying
x2 = 3x + 5

Reorder the terms:
x2 = 5 + 3x

Solving
x2 = 5 + 3x

Solving for variable 'x'.

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

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

Combine like terms: 5 + -5 = 0
-5 + -3x + x2 = 0 + 3x + -3x
-5 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-5 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3x + 5 + x2 = 0 + 5

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

Combine like terms: -5 + 5 = 0
0 + -3x + x2 = 0 + 5
-3x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3x + x2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3x + x2 = 7.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -1.5 = 2.692582404 Simplifying x + -1.5 = 2.692582404 Reorder the terms: -1.5 + x = 2.692582404 Solving -1.5 + x = 2.692582404 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 = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.692582404 + 1.5 x = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 x = 4.192582404 Simplifying x = 4.192582404

Subproblem 2

x + -1.5 = -2.692582404 Simplifying x + -1.5 = -2.692582404 Reorder the terms: -1.5 + x = -2.692582404 Solving -1.5 + x = -2.692582404 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 = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.692582404 + 1.5 x = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 x = -1.192582404 Simplifying x = -1.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.192582404, -1.192582404}

See similar equations:

| 12y-5=2 | | 4a+4=8 | | 3x^2+17x-6= | | 3x^2+17-6= | | 2X+35-15=20 | | 49-64x^2=0 | | 5n+25g=5.65 | | -7x-3y-2+7x= | | x+5y=57 | | x+5y= 57 | | -3x+4y=76 | | -6b+13b= | | 12b+3+2=20 | | n=2(l+w)-4 | | 3-(Inj(1))=3a | | 9c+7=21 | | 5x^6-125X^4=0 | | 7y=4y+8 | | 3-In(1)=3a | | -(-4)= | | 12a-7=15 | | 4y=7y+8 | | 8i+4=10 | | -5x-3x+x= | | 14x-2(x-9)+21= | | 3(2x-2)-2(3x+4)= | | 3-3u=4-2u | | 4(a+9)-12= | | 5+2*(2x-4)= | | x^3-100x=0 | | 2-(5-x)+3(-2x)= | | 5*(3x+2)= |

Equations solver categories